Abstract:
Disclosed is an encoding apparatus that can efficiently encode a signal that is a broad or extra-broad band signal or the like, thereby improving the quality of a decoded signal. This encoding apparatus includes a band establishing unit ( 301 ) that generate, based on the characteristic of the input signal, band establishment information to be used for dividing the band of the input signal to establish a first band part of lower frequency side and a second band part of higher frequency side; a lower frequency encoding unit ( 302 ) for encoding, based on the band establishment information, the input signal of the first band part to generate encoded lower frequency part information; and a higher frequency encoding unit ( 303 ) for encoding, based on the band establishment information, the input signal of the second band part to generate encoded higher frequency part information.

Description:
TECHNICAL FIELD 
     The present invention relates to an encoding apparatus, decoding apparatus, and methods thereof, used in a communication system that encodes and transmits a signal. 
     BACKGROUND ART 
     When a speech or music signal is transmitted in a packet communication system typified by Internet communication, a mobile communication system, or the like, compression and encoding technologies are often used in order to increase the transmission efficiency of the speech or music signal. In recent years, while a speech or music signal is simply encoded at a low bit rate, there has been a growing need for a technology that encodes a wider-band speech or music signal. 
     In response to such a need, various technologies have been developed that encode a wideband speech or music signal without greatly increasing the amount of information after encoding. For example, Patent Literature 1 discloses a technology whereby a characteristic of a frequency high-band part among spectral data obtained by converting an input audio signal of a fixed time is generated as auxiliary information, and this is output together with low-band part coded information. 
     CITATION LIST 
     Patent Literature 
     PTL 1 
     
         
         Japanese Patent Application Laid-Open No. 2003-255973
 
PTL 2
 
         WO 2007/052088 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, with the band enhancement technology disclosed in above Patent Literature 1, a low-band part of an input signal and a high-band part generated using auxiliary information are decided beforehand in a fixed manner. Therefore, since the same coding method is used when high-band part spectral data of an input signal is minute, or conversely when high-band part spectral data has extremely high energy, or when high-band part spectral data has a complex waveform, for example, there is a problem of coding efficiency not being high. When auxiliary information is encoded at a low bit rate, in particular, the quality of decoded speech generated using calculated auxiliary information is inadequate, and in some cases there is a possibility of an allophone being generated. 
     It is an object of the present invention to provide an encoding apparatus, decoding apparatus, and methods thereof that enable coding of high-band part spectral data to be performed efficiently, based on low-band part spectral data, for a signal such as a wideband signal (7 kHz band) or ultrawideband signal (14 kHz band), and enable the quality of a decoded signal to be improved. 
     Solution to Problem 
     One aspect of an encoding apparatus according to the present invention performs band enhancement using a low-band side spectrum and generates a high-band side spectrum, and employs a configuration comprising: a band setting section that inputs an input signal of the frequency domain and uses a characteristic of the input signal of the frequency domain as a basis, or inputs an input signal of the frequency domain and a coding parameter and uses the coding parameter and/or a characteristic of the input signal of the frequency domain as a basis, for generating band setting information that decides a first band of a high-band side set by the band enhancement; and a high-band coding section that encodes the input signal of the first band decided based on the band setting information and generates high-band part coded information. 
     One aspect of a decoding apparatus according to the present invention receives and decodes coded information generated by an encoding apparatus that performs band enhancement using a low-band side spectrum of an input signal of a frequency domain and generates a high-band side spectrum, and employs a configuration comprising: a reception section that receives coded information including high-band part coded information generated by encoding an input signal of a first band that is a high-band side of the frequency domain, low-band part coded information generated by encoding the input signal of a second band of a low-band side of the frequency domain, and band setting information of the first band set based on a characteristic of an input signal of the frequency domain and/or a coding parameter included in the coded information; a low-band decoding section that generates a low-band decoded signal for the second band using the low-band part coded information; and a high-band decoding section that generates a high-band decoded signal for the first band using the high-band part coded information and the band setting information, and generates a decoded signal of the frequency domain using the low-band decoded signal and the high-band decoded signal. 
     One aspect of a coding method according to the present invention performs band enhancement using a low-band side spectrum and generates a high-band side spectrum, and comprises: a band setting step of inputting an input signal of the frequency domain and using a characteristic of the input signal of the frequency domain as a basis, or inputting an input signal of the frequency domain and a coding parameter and using the coding parameter and/or a characteristic of the input signal of the frequency domain as a basis, for generating band setting information that decides a first band of a high-band side set by the band enhancement; and a high-band encoding step of encoding the input signal of the first band decided based on the band setting information and generating high-band part coded information. 
     One aspect of a decoding method according to the present invention receives and decodes coded information generated by an encoding apparatus that performs band enhancement using a low-band side spectrum of an input signal of the frequency domain and generates a high-band side spectrum, and comprises: a receiving step of receiving coded information including high-band part coded information generated by encoding an input signal of a first band that is a high-band side of the frequency domain, low-band part coded information generated by encoding the input signal of a second band of a low-band side of the frequency domain, and band setting information of the first band set based on a characteristic of an input signal of the frequency domain and/or a coding parameter included in the coded information; a low-band decoding step of generating a low-band decoded signal for the second band using the low-band part coded information; and a high-band decoding step of generating a high-band decoded signal for the first band using the high-band part coded information and the band setting information, and generating a decoded signal of the frequency domain using the low-band decoded signal and the high-band decoded signal. 
     Advantageous Effects of Invention 
     The present invention enables coding of high-band part spectral data such as a wideband signal or an ultrawideband signal to be performed efficiently, and enables the quality of a decoded signal to be improved. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram showing the configuration of a communication system having an encoding apparatus and decoding apparatus according to Embodiment 1 of the present invention; 
         FIG. 2  is a block diagram showing the internal principal-part configuration of the encoding apparatus shown in  FIG. 1 ; 
         FIG. 3  is a block diagram showing the internal principal-part configuration of the coding section shown in  FIG. 2 ; 
         FIG. 4  is a block diagram showing the internal principal-part configuration of the low-band coding section shown in  FIG. 3 ; 
         FIG. 5  is a block diagram showing the internal principal-part configuration of the high-band coding section shown in  FIG. 3 ; 
         FIG. 6  is a drawing for explaining details of filtering processing by the filtering section shown in  FIG. 5 ; 
         FIG. 7  is a flowchart showing the processing procedure for finding optimal pitch coefficient T p ′ for subband SB p  in the search section shown in  FIG. 5 ; 
         FIG. 8  is a block diagram showing the internal principal-part configuration of the decoding apparatus shown in  FIG. 1 ; 
         FIG. 9  is a block diagram showing the internal principal-part configuration of the decoding section shown in  FIG. 8 ; 
         FIG. 10  is a block diagram showing the internal principal-part configuration of the low-band decoding section shown in  FIG. 9 ; 
         FIG. 11  is a block diagram showing the internal principal-part configuration of the high-band decoding section shown in  FIG. 9 ; 
         FIG. 12  is a block diagram showing the internal principal-part configuration of an encoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 13  is a block diagram showing the internal principal-part configuration of the second layer coding section shown in  FIG. 12 ; 
         FIG. 14  is a block diagram showing the internal principal-part configuration of the low-band coding section shown in  FIG. 13 ; 
         FIG. 15  is a block diagram showing the internal principal-part configuration of the high-band coding section shown in  FIG. 13 ; 
         FIG. 16  is a block diagram showing the internal principal-part configuration of a decoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 17  is a block diagram showing the internal principal-part configuration of the second layer decoding section shown in  FIG. 16 ; 
         FIG. 18  is a block diagram showing the internal principal-part configuration of the high-band decoding section shown in  FIG. 17 ; 
         FIG. 19  is a block diagram showing the internal principal-part configuration of an encoding apparatus according to Embodiment 3 of the present invention; 
         FIG. 20  is a block diagram showing the internal principal-part configuration of the second layer coding section shown in  FIG. 19 ; 
         FIG. 21  is a block diagram showing the internal principal-part configuration of the high-band coding section shown in  FIG. 20 ; 
         FIG. 22  is a block diagram showing the internal principal-part configuration of a decoding apparatus according to Embodiment 3 of the present invention; 
         FIG. 23  is a block diagram showing the internal principal-part configuration of the second layer decoding section shown in  FIG. 22 ; 
         FIG. 24  is a block diagram showing the internal principal-part configuration of an encoding apparatus according to Embodiment 4 of the present invention; 
         FIG. 25  is a block diagram showing the internal principal-part configuration of the second layer coding section shown in  FIG. 24 ; 
         FIG. 26  is a block diagram showing the internal principal-part configuration of the band enhancement coding section shown in  FIG. 25 ; 
         FIG. 27  is a block diagram showing the internal principal-part configuration of the residual spectrum coding section shown in  FIG. 25 ; 
         FIG. 28  is a drawing showing conceptually a correspondence relationship between an encoded/decoded spectrum band and amount of information (coding bit rate) in each layer; 
         FIG. 29  is a block diagram showing the internal principal-part configuration of a decoding apparatus according to Embodiment 4 of the present invention; 
         FIG. 30  is a block diagram showing the internal principal-part configuration of the second layer decoding section shown in  FIG. 29 ; 
         FIG. 31  is a block diagram showing the internal principal-part configuration of the residual spectrum decoding section shown in  FIG. 30 ; 
         FIG. 32  is a block diagram showing the internal principal-part configuration of the band enhancement decoding section shown in  FIG. 30 ; and 
         FIG. 33  is a drawing showing conceptually another correspondence relationship between an encoded/decoded spectrum band and amount of information (coding bit rate) in each layer; 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Now, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following descriptions, a speech encoding apparatus and speech decoding apparatus are taken as examples of an encoding apparatus and decoding apparatus according to the present invention. 
     Embodiment 1 
       FIG. 1  is a block diagram showing the configuration of a communication system having an encoding apparatus and decoding apparatus according to Embodiment 1 of the present invention. In  FIG. 1 , the communication system is provided with encoding apparatus  101  and decoding apparatus  103 , which are able to communicate via channel  102 . Both encoding apparatus  101  and channel  102  are normally used and installed in a base station apparatus, communication terminal apparatus, or the like. 
     Encoding apparatus  101  divides an input signal into N samples at a time (where N is a natural number), takes N samples as one frame, and performs coding on a frame-by-frame basis. Here, an input signal subject to coding will be expressed as x n  (n=0, . . . , N−1). Here, n indicates the (n+1)th signal element in a signal divided into N samples at a time. Encoding apparatus  101  transmits encoded input information (hereinafter referred to as “coded information”) to decoding apparatus  103  via channel  102 . 
     Decoding apparatus  103  receives coded information transmitted from encoding apparatus  101  via channel  102 , decodes this coded information, and obtains an output signal. 
       FIG. 2  is a block diagram showing the internal principal-part configuration of encoding apparatus  101  shown in  FIG. 1 . Encoding apparatus  101  mainly comprises orthogonal transform processing section  201  and coding section  202 . 
     Orthogonal transform processing section  201  has internal buffers buf 1   n  (n=0, . . . , N−1), and performs a Modified Discrete Cosine Transform (MDCT) on input signal x n . 
     Next, orthogonal transform processing by orthogonal transform processing section  201  will be described in relation to its computational procedure and data output to an internal buffer. 
     First, orthogonal transform processing section  201  initializes buffer buf 1   n  with “0” as an initial value by means of equation 1 below.
 
[1]
 
buf1 n =0( n= 0, . . .  N− 1)  (Equation 1)
 
     Then, orthogonal transform processing section  201  performs a modified discrete cosine transform (MDCT) on input signal x n , and finds input signal MDCT coefficient (hereinafter referred to as input spectrum) X(k), in accordance with equation 2 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             X 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               2 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   x 
                                   n 
                                   ′ 
                                 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         
                                           ( 
                                           
                                             
                                               2 
                                               ⁢ 
                                               n 
                                             
                                             + 
                                             1 
                                             + 
                                             N 
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               2 
                                               ⁢ 
                                               k 
                                             
                                             + 
                                             1 
                                           
                                           ) 
                                         
                                         ⁢ 
                                         π 
                                       
                                       
                                         4 
                                         ⁢ 
                                         N 
                                       
                                     
                                     ] 
                                   
                                 
                               
                             
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               k 
                               = 
                               0 
                             
                             , 
                             … 
                             ⁢ 
                             
                                 
                             
                             , 
                             
                               N 
                               - 
                               1 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                           
                       
                     
                   
                 
               
               
                 
                   [ 
                   2 
                   ] 
                 
               
             
           
         
       
     
     Here, k indicates an index of each sample in one frame. Orthogonal transform processing section  201  finds vector x n ′ linking input signal x n  and buffer buf 1   n  by means of equation 3 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     x 
                     n 
                     ′ 
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             buf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               1 
                               n 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 0 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             x 
                             
                               n 
                               - 
                               N 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 N 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   3 
                   ] 
                 
               
             
           
         
       
     
     Orthogonal transform processing section  201  then updates buffer buf 1   n  by means of equation 4.
 
[4]
 
buf1 n   =x   n ( n= 0, . . .  N− 1)  (Equation 4)
 
     Then orthogonal transform processing section  201  outputs input spectrum X(k) to coding section  202 . 
     Input spectrum X(k) is input to coding section  202  from orthogonal transform processing section  201 . Coding section  202  encodes input spectrum X(k), and generates coded information. Then coding section  202  transmits the generated coded information to decoding apparatus  103  via channel  102 . 
       FIG. 3  is a block diagram showing the internal principal-part configuration of coding section  202  shown in  FIG. 2 . Details of the processing performed by coding section  202  will now be described with reference to  FIG. 3 . Coding section  202  mainly comprises band setting section  301 , low-band coding section  302 , high-band coding section (band enhancement section)  303 , and multiplexing section  304 . These sections perform the following operations. 
     Input spectrum X(k) is input to band setting section  301  from orthogonal transform processing section  201 . Band setting section  301  analyzes the spectral characteristics of input spectrum X(k), and sets bands subject to coding by low-band coding section  302  and high-band coding section (band enhancement section)  303  respectively according to the analysis results. Then, band setting section  301  outputs band setting information indicating the set bands to low-band coding section  302 , high-band coding section  303 , and multiplexing section  304 . 
     The band setting information calculation method used by band setting section  301  will now be described. 
     Band setting section  301  first calculates, for input spectrum X(k), energy (low-band energy) E Low  of a part for which the band is less than or equal to TH Low  in accordance with equation 5-1, and energy (high-band energy) E High  of a part for which the band is greater than or equal to TH High  in accordance with equation 5-2, where TH Low  and TH High  are predetermined threshold values, and TH Low &lt;TH High . In equation 5-2, F max  is the maximum band value (maximum frequency value). 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     Low 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       
                         TH 
                         Low 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     High 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         
                           TH 
                           High 
                         
                       
                       Fmax 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Next, band setting section  301  compares the magnitude of low-band energy E Low  calculated by means of equation 5-1 with the magnitude of high-band energy E High  calculated by means of equation 5-2, and decides band setting information Band_Setting in accordance with equation 6 below. That is to say, based on input spectrum energy characteristics, band setting section  301  generates band setting information for dividing the input spectrum band and setting a band on the low-band side (low-band part) and the high-band side (high-band part). Here, γ in equation 6 is a predetermined constant. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Band_setting 
                   = 
                   
                     { 
                     
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 if 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   E 
                                   Low 
                                 
                               
                               ≥ 
                               
                                 γ 
                                 · 
                                 
                                   E 
                                   High 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           1 
                         
                         
                           
                             ( 
                             else 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
           
         
       
     
     That is to say, band setting section  301  sets the band setting information Band_Setting value to 0 if low-band energy E Low  is somewhat greater than high-band energy E High , and sets the band setting information Band_Setting value to 1 otherwise. Band setting section  301  outputs decided band setting information Band_Setting to low-band coding section  302 , high-band coding section  303 , and multiplexing section  304 . 
     Input spectrum X(k) is input to low-band coding section  302  from orthogonal transform processing section  201 . Also, band setting information Band_Setting is input to low-band coding section  302  from band setting section  301 . Based on band setting information Band_Setting, low-band coding section  302  encodes input spectrum X(k) and generates low-band part coded information. Then low-band coding section  302  outputs the low-band part coded information to multiplexing section  304 . Details of the processing performed by low-band coding section  302  will be given later herein. 
     Input spectrum X(k) is input to high-band coding section  303  from orthogonal transform processing section  201 . Also, band setting information Band_Setting is input to high-band coding section  303  from band setting section  301 . Based on band setting information Band_Setting, high-band coding section  303  encodes input spectrum X(k) and generates high-band part coded information (band enhancement information). Then high-band coding section  303  outputs the high-band part coded information to multiplexing section  304 . Details of the processing performed by high-band coding section  303  will be given later herein. 
     Multiplexing section  304  multiplexes band setting information, low-band part coded information, and high-band part coded information input from band setting section  301 , low-band coding section  302 , and high-band coding section  303  respectively, and outputs the multiplexed information to channel  102  as coded information. 
       FIG. 4  is a block diagram showing the internal configuration of low-band coding section  302 . Low-band coding section  302  mainly comprises coding target spectrum calculation section  401 , shape coding section  402 , gain coding section  403 , and multiplexing section  404 . These sections perform the following operations. 
     Band setting information Band_Setting is input to coding target spectrum calculation section  401  from band setting section  301 . Also, input spectrum X(k) is input to coding target spectrum calculation section  401  from orthogonal transform processing section  201 . Based on the band setting information Band_Setting value, coding target spectrum calculation section  401  decides a band that is to be an coding target, and outputs only the spectrum of the corresponding band within input spectrum X(k) to shape coding section  402 . 
     Specifically, if the band setting information Band_Setting value is 0, coding target spectrum calculation section  401  outputs a spectrum for which the band is less than or equal to Max 1  (k≦Max 1 ) within input spectrum X(k) to shape coding section  402  as coding target spectrum X′(k). Also, if the band setting information Band_Setting value is 1, coding target spectrum calculation section  401  outputs a spectrum for which the band is less than or equal to Max 2  (k≦Max 2 ) within input spectrum X(k) to shape coding section  402  as coding target spectrum X′(k). 
     Here, the relationship between Max 1  and Max 2  is assumed to be Max 1 &lt;Max 2 . That is to say, if the band setting information Band_Setting value is 0, coding target spectrum calculation section  401  selects a spectrum on the lower-band side within input spectrum X(k) as coding target spectrum X′(k). On the other hand, if the band setting information Band_Setting value is 1, coding target spectrum calculation section  401  selects a spectrum of a part for which the bandwidth is greater than when the band setting information Band_Setting value is 0 within input spectrum X(k) as coding target spectrum X′(k). 
     Shape coding section  402  performs shape quantization on a subband-by-subband basis on coding target spectrum X′(k) input from coding target spectrum calculation section  401 . Specifically, shape coding section  402  first divides coding target spectrum X′(k) into L subbands. Then, for each of the L subbands, shape coding section  402  searches an internal shape codebook comprising SQ shape code vectors, and finds an index of a shape code vector for which evaluation measure Shape_q(i) in equation 7 below is maximal. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Shape_q 
                       ⁢ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           { 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 BW 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       + 
                                       
                                         BS 
                                         ⁡ 
                                         
                                           ( 
                                           j 
                                           ) 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 · 
                                 
                                   SC 
                                   k 
                                   i 
                                 
                               
                               ) 
                             
                           
                           } 
                         
                         2 
                       
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             BW 
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             SC 
                             k 
                             i 
                           
                           · 
                           
                             SC 
                             k 
                             i 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         L 
                         - 
                         1 
                       
                       , 
                       
                         i 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         SQ 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   7 
                   ] 
                 
               
             
           
         
       
     
     In this equation, SC i   k  indicates a shape code vector configuring a shape codebook, i indicates a shape code vector index, and k indicates a shape code vector element index. Also, BW(j) represents the bandwidth of a band for which the band index is j, and BS(j) represents the minimum index of a spectrum configuring a band for which the band index is j. 
     Shape coding section  402  outputs shape code vector index S_max for which evaluation measure Shape_q(i) in equation 7 above is maximal to multiplexing section  404  as shape coded information. Also, shape coding section  402  calculates ideal gain Gain_i(j) in accordance with equation 8 below, and outputs this to gain coding section  403 . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Gain_i 
                       ⁢ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             BW 
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 X 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   + 
                                   
                                     BS 
                                     ⁡ 
                                     
                                       ( 
                                       j 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                             · 
                             
                               SC 
                               k 
                               
                                 S 
                                 ⁢ 
                                 _ 
                                 ⁢ 
                                 max 
                               
                             
                           
                           ) 
                         
                       
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             BW 
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             SC 
                             k 
                             
                               S 
                               ⁢ 
                               _ 
                               ⁢ 
                               max 
                             
                           
                           · 
                           
                             SC 
                             k 
                             
                               S 
                               ⁢ 
                               _ 
                               ⁢ 
                               max 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         L 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   8 
                   ] 
                 
               
             
           
         
       
     
     Gain coding section  403  directly quantizes ideal gain Gain_i(j) input from shape coding section  402  in accordance with equation 9 below. Here too, gain coding section  403  treats an ideal gain as an L-dimensional vector, searches an internal gain codebook comprising GQ gain code vectors, and performs vector quantization. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Gain_q 
                       ⁢ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     = 
                     
                       
                         { 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               0 
                             
                             
                               L 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 Gain_i 
                                 ⁢ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                               - 
                               
                                 GC 
                                 j 
                                 i 
                               
                             
                             } 
                           
                         
                         } 
                       
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         i 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         GQ 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   9 
                   ] 
                 
               
             
           
         
       
     
     Gain coding section  403  finds gain code vector index G_min that minimizes square error Gain_q(i) in equation 9 above. Gain coding section  403  outputs G_min to multiplexing section  404  as gain coded information. 
     Multiplexing section  404  multiplexes shape coded information S_max input from shape coding section  402  and gain coded information G_min input from gain coding section  403 , and outputs the multiplexed information to multiplexing section  304  as low-band part coded information. Shape coded information and gain coded information may also be directly input to multiplexing section  304 , and multiplexed with high-band part coded information by multiplexing section  304 . 
     This concludes a description of the configuration of low-band coding section  302 . 
       FIG. 5  is a block diagram showing the internal configuration of high-band coding section  303 . High-band coding section  303  is provided with band division section  501 , filter state setting section  502 , filtering section  503 , search section  505 , pitch coefficient setting section  504 , gain coding section  506 , and multiplexing section  507 . These sections perform the following operations. 
     Input spectrum X(k) is input to band division section  501  from orthogonal transform processing section  201 . Also, band setting information Band_Setting is input to band division section  501  from band setting section  301 . Band division section  501  divides a high-band part of input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1) according to the band setting information Band_Setting value. Then, band division section  501  outputs bandwidth BW p  (p=0, 1, . . . , P−1) and initial index BS p  (p=0, 1, . . . , P−1) of each subband to filtering section  503 , search section  505 , and multiplexing section  507  as band division information. 
     Specifically, if the band setting information Band_Setting value is 0, band division section  501  divides a part for which the band is greater than or equal to Max 1  (Max 1 ≦k&lt;Fmax) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). Also, if the band setting information Band_Setting value is 1, band division section  501  divides a part for which the band is greater than or equal to Max 2  (Max 2 ≦k&lt;Fmax) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). Here, Fmax is the maximum band value. Also, below, a part in subband SB p  within input spectrum X(k) is denoted as subband spectrum X p (k) (BS p ≦k&lt;BS p +BW p ). 
     Filter state setting section  502  sets input spectrum X(k) input from orthogonal transform processing section  201  as a filter state used by filtering section  503 . Input spectrum X(k) is stored as a filter internal state (filter state) in an entire frequency band 0≦k&lt;Fmax spectrum S(k) (0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 ) band in filtering section  503 . Filter state setting section  502  outputs the set filter state to filtering section  503 . 
     Filtering section  503  is provided with a multi-tap pitch filter (that is, the number of taps is greater than 1). Filtering section  503  calculates input spectrum estimated value S′(k) (FL≦k≦FH) (hereinafter referred to as estimated spectrum) by filtering input spectrum X(k) based on the filter state set by filter state setting section  502  and pitch coefficient T input from pitch coefficient setting section  504 . Filtering section  503  outputs estimated spectrum S′(k) to search section  505 . Details of the filtering processing performed by filtering section  503  will be given later herein. 
     Search section  505  calculates similarity of a high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) divided by band division section  501  for input spectrum X(k) input from orthogonal transform processing section  201  and estimated spectrum S′(k) input from filtering section  503 . This similarity calculation is performed by means of a correlation computation or the like, for example. 
     The processing of filtering section  503 , search section  505 , and pitch coefficient setting section  504  forms a closed loop. In this closed loop, search section  505  calculates similarity corresponding to each pitch coefficient by variously changing pitch coefficient T input to filtering section  503  from pitch coefficient setting section  504 . Then, of the calculated similarities, search section  505  outputs the pitch coefficient for which similarity is maximal to multiplexing section  507  as optimum pitch coefficient T′. Also, search section  505  outputs estimated spectrum S′(k) to gain coding section  506 . 
     Under the control of search section  505 , pitch coefficient setting section  504  gradually changes pitch coefficient T within the search range (Tmin≦T≦Tmax), and successively outputs post-change pitch coefficient T to filtering section  503 . 
     Gain coding section  506  calculates gain information of a high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) divided by band division section  501  for input spectrum X(k) input from orthogonal transform processing section  201 . Specifically, gain coding section  506  divides a high-band part frequency band ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) into J samples, and finds the spectral power of each subband of input spectrum X(k). In this case, spectral power B(j) of the j&#39;th subband is expressed by equation 10 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       B 
                       ⁡ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             BL 
                             j 
                           
                         
                         
                           BH 
                           j 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   10 
                   ] 
                 
               
             
           
         
       
     
     In equation 10, BL j  represents the minimum frequency of the j&#39;th subband, and BM j  represents the maximum frequency of the j&#39;th subband. Also, gain coding section  506  similarly calculates spectral power B′(j) of each subband of estimated spectrum S′(k) input from search section  505  in accordance with equation 11 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         B 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             BL 
                             j 
                           
                         
                         
                           BH 
                           j 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             S 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   11 
                   ] 
                 
               
             
           
         
       
     
     Gain coding section  506  then calculates variation V(j) of each subband for input spectrum X(k) in accordance with equation 12 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       V 
                       ⁡ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           B 
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         
                           
                             B 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   12 
                   ] 
                 
               
             
           
         
       
     
     Then, using an internal gain encoding codebook, gain coding section  506  encodes variation V(j), and outputs an index corresponding to post-coding variation V q (j) to multiplexing section  507 . 
     Multiplexing section  507  multiplexes optimum pitch coefficient T′ input from search section  505  and an index of variation V(j) input from gain coding section  506  as high-band part coded information, and outputs the multiplexed information to multiplexing section  304 . Optimum pitch coefficient T′ and a variation V(j) index may also be directly input to multiplexing section  304 , and multiplexed with low-band part coded information by multiplexing section  304 . 
     Details of the filtering processing performed by filtering section  503  will now be described with reference to  FIG. 6 . 
     Filtering section  503  generates spectrum S(k) of a ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) band using pitch coefficient T input from pitch coefficient setting section  504  according to band division by band division section  501 . Filtering section  503  transfer function F(z) is expressed by equation 13 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     F 
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       1 
                       - 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             
                               - 
                               M 
                             
                           
                           M 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             β 
                             i 
                           
                           ⁢ 
                           
                             z 
                             
                               
                                 - 
                                 T 
                               
                               + 
                               i 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   13 
                   ] 
                 
               
             
           
         
       
     
     In equation 13, T represents a pitch coefficient provided by pitch coefficient setting section  504 , and β i  represents a filter coefficient stored internally beforehand. Also, in equation 13, M is an indicator relating to the number of taps, with M=1 being set, for example, when the number of taps is 3. When the number of taps is 3, (β −1 , β 0 , β 1 )=(0.1, 0.8, 0.1) may be given as an example of filter coefficient candidates. Other values, such as (β −1 , β 0 , β 1 )=(0.2, 0.6, 0.2), (0.3, 0.4, 0.3), are also applicable. 
     First, input spectrum X(k) is stored as a filter internal state (filter state) in a (0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 ) band of spectrum S(k) of the entire frequency band in filtering section  503 . 
     Also, estimated spectrum S′(k) is stored in a spectrum S(k) high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) by means of the following filtering processing procedure. In estimated spectrum S′(k), spectrum S(k−T) of a frequency that is T lower than this k is basically assigned to estimated spectrum S′(k). Actually, however, in order to increase spectrum smoothness, spectrum β i ·S(k−T+i) obtained by multiplying nearby spectrum S(k−T+i) demultiplexed by i from spectrum S(k−T) by predetermined filter coefficient β i  is added for all i&#39;s and the obtained spectrum is assigned to S′(k). This processing is expressed by equation 14 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       S 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           - 
                           1 
                         
                       
                       1 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         β 
                         i 
                       
                       · 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               T 
                               + 
                               i 
                             
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   14 
                   ] 
                 
               
             
           
         
       
     
     Filtering section  503  calculates estimated spectrum S′(k) in a high-band part frequency band ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) by performing the above computation while changing k in the band Max 1 ≦k&lt;Fmax or band Max 2 ≦k&lt;Fmax range in order from low-frequency k=Max 1  or k=Max 2 . 
     The above filtering processing is performed after zeroizing spectrum S(k) in the high-band part frequency band ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) range each time pitch coefficient T is provided from pitch coefficient setting section  504 . That is to say, each time pitch coefficient T changes, spectrum S(k) is calculated and is output to search section  505 . 
       FIG. 7  is a flowchart showing the processing procedure for finding optimal pitch coefficient T p ′ for subband SB p  in search section  505 . By repeating the procedure shown in  FIG. 7 , search section  505  finds optimal pitch coefficient T p ′ (p=0, 1, . . . , P−1) corresponding to each subband SB p  (p=0, 1, . . . , P−1). 
     First, search section  505  initializes minimum similarity D min , which is a variable for saving a minimum similarity value, to “+∞” (ST 2010 ). Then search section  505  calculates similarity D between an input spectrum X(k) high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) and estimated spectrum S′(k) for a certain pitch coefficient in accordance with equation 15 below (ST 2020 ). 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       15 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   D 
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           M 
                           ′ 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             
                               
                                 BS 
                                 p 
                               
                               + 
                               k 
                             
                             ) 
                           
                         
                         · 
                         
                           X 
                           ⁡ 
                           
                             ( 
                             
                               
                                 BS 
                                 p 
                               
                               + 
                               k 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   M 
                                   ′ 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   X 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         BS 
                                         p 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                                 · 
                                 
                                   
                                     S 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         BS 
                                         p 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               M 
                               ′ 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               
                                 S 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     BS 
                                     p 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                             · 
                             
                               
                                 S 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     BS 
                                     p 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           0 
                           &lt; 
                           
                             M 
                             ′ 
                           
                           ≤ 
                           
                             BW 
                             p 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   15 
                   ] 
                 
               
             
           
         
       
     
     In equation 15, M′ indicates the number of samples when calculating similarity D, and may be any value less than or equal to the bandwidth of each subband. 
     Next, search section  505  determines whether or not calculated similarity D is smaller than minimum similarity D min , (ST 2030 ). If similarity D calculated in ST 2020  is smaller than minimum similarity D min  (ST 2030 : “YES”), search section  505  assigns similarity D to minimum similarity D min  (ST 2040 ). On the other hand, if similarity D calculated in ST 2020  is greater than or equal to minimum similarity (ST 2030 : “NO”), search section  505  determines whether or not the search range has ended (ST 2050 ). That is to say, search section  505  determines whether or not similarity D has been calculated in accordance with equation 15 above in ST 2020  for all pitch coefficients within the search range. If the search range has not ended (ST 2050 : “NO”), search section  505  returns to ST 2020  again. Then search section  505  calculates similarity D in accordance with equation 15 for a different pitch coefficient from that when similarity D was calculated in accordance with equation 15 in the previous ST 2020  procedure. On the other hand, if the search range has ended (ST 2050 : “YES”), search section  505  outputs pitch coefficient T corresponding to minimum similarity D min  to multiplexing section  507  as optimum pitch coefficient T p ′ (ST 2060 ). 
     This concludes a description of the processing performed by high-band coding section  303 . 
     This concludes a description of the configuration of encoding apparatus  101 . 
     Decoding apparatus  103  shown in  FIG. 1  will now be described. 
       FIG. 8  is a block diagram showing the internal principal-part configuration of decoding apparatus  103 . Decoding apparatus  103  mainly comprises decoding section  801  and orthogonal transform processing section  802 . These sections perform the following operations. 
     Coded information transmitted from encoding apparatus  101  via channel  102  is input to decoding section  801 . Decoding section  801  decodes the input coded information, and outputs spectral data obtained by decoding (a decoded spectrum) to orthogonal transform processing section  802 . Details of the processing performed by decoding section  801  will be given later herein. 
     The spectral data (decoded spectrum) is input to orthogonal transform processing section  802  from decoding section  801 . Orthogonal transform processing section  802  executes an orthogonal transform on the spectral data (decoded spectrum), and converts it to a time-domain signal. Orthogonal transform processing section  802  outputs the obtained signal as an output signal. Details of the processing performed by orthogonal transform processing section  802  will be given later herein. 
       FIG. 9  is a block diagram showing the internal configuration of decoding section  801  shown in  FIG. 8 . Decoding section  801  mainly comprises demultiplexing section  901 , low-band decoding section  902 , and high-band decoding section (band enhancement section)  903 . 
     Coded information transmitted from encoding apparatus  101  via channel  102  is input to demultiplexing section  901 . Demultiplexing section  901  demultiplexes the coded information into low-band part coded information, high-band part coded information, and band setting information. Then demultiplexing section  901  outputs the low-band part coded information to low-band decoding section  902 , outputs the high-band part coded information (band enhancement information) to high-band decoding section  903 , and outputs the band setting information to low-band decoding section  902  and high-band decoding section  903 . 
     Low-band part coded information and band setting information are input to low-band decoding section  902  from demultiplexing section  901 . Low-band decoding section  902  generates a low-band part decoded spectrum from the input low-band part coded information and band setting information, and outputs the generated low-band part decoded spectrum to high-band decoding section  903 . Details of the processing performed by low-band decoding section  902  will be given later herein. 
     High-band part coded information and band setting information are input to high-band decoding section  903  from demultiplexing section  901 . Also, a low-band part decoded spectrum is input to high-band decoding section  903  from low-band decoding section  902 . High-band decoding section  903  generates a decoded spectrum from the input low-band part decoded spectrum, high-band part coded information, and band setting information, and outputs the generated decoded spectrum to orthogonal transform processing section  802 . Details of the processing performed by high-band decoding section  903  will be given later herein. 
       FIG. 10  is a block diagram showing the internal configuration of low-band decoding section  902 . Low-band decoding section  902  mainly comprises demultiplexing section  911 , shape decoding section  912 , and gain decoding section  913 . These sections perform the following operations. 
     Demultiplexing section  911  demultiplexes low-band part coded information input from demultiplexing section  901  into shape coded information S_max and gain coded information G_min, and outputs post-demultiplexing shape coded information S_max to shape decoding section  912 , and outputs gain coded information G_min to gain decoding section  913 . Provision may also be made for shape coded information and gain coded information to be demultiplexed from coded information directly by demultiplexing section  901 . 
     Shape decoding section  912  incorporates a shape codebook of the same kind as the shape codebook with which shape coding section  402  of low-band coding section  302  is provided, and searches the shape codebook with shape coded information S_max input from demultiplexing section  911  as an index. Shape decoding section  912  outputs a found shape code vector to gain decoding section  913  as a shape value of an coding target band spectrum indicated by band setting information Band_Setting input from demultiplexing section  901 . Here, a shape code vector found as a shape value is denoted as Shape_q′(k). 
     Gain decoding section  913  incorporates a gain codebook of the same kind as the gain codebook with which gain coding section  403  of low-band coding section  302  is provided, and uses this gain codebook to perform inverse quantization of a gain value from gain coded information in accordance with equation 16 below. Here too, a gain value is treated as an L-dimensional vector, and vector inverse quantization is performed. That is to say, gain code vector GC j   G     —     min  corresponding to gain coded information G_min is taken directly as gain value Gain_q′(j).
 
[16]
 
Gain —   q′ ( j )= GC   j   G     —     min ( j= 0, . . . , L− 1)  (Equation 16)
 
     Then, using a gain value obtained by inverse quantization and a shape value input from shape decoding section  912 , gain decoding section  913  calculates low-band part decoded spectrum S 1 ( k ) in accordance with equation 17 below, and outputs calculated low-band part decoded spectrum S 1 ( k ) to high-band decoding section  903 . In spectrum (MDCT coefficient) inverse quantization, if k is present in B(j″) through B(j″+1)−1, gain value Gain_q′(j) has the value of Gain_q′(j″). 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       Gain_q 
                       ′ 
                     
                     ⁢ 
                     
                       
                         ( 
                         j 
                         ) 
                       
                       · 
                       
                         Shape_q 
                         ′ 
                       
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 k 
                                 = 
                                 
                                   BL 
                                   j 
                                 
                               
                               , 
                               … 
                               ⁢ 
                               
                                   
                               
                               , 
                               
                                 BH 
                                 j 
                               
                             
                           
                         
                         
                           
                             
                               
                                 j 
                                 = 
                                 0 
                               
                               , 
                               … 
                               ⁢ 
                               
                                   
                               
                               , 
                               
                                 L 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   17 
                   ] 
                 
               
             
           
         
       
     
       FIG. 11  is a block diagram showing the internal configuration of high-band decoding section  903 . High-band decoding section  903  mainly comprises demultiplexing section  921 , filter state setting section  922 , filtering section  923 , gain decoding section  924 , and spectrum adjustment section  925 . These sections perform the following operations. 
     Demultiplexing section  921  demultiplexes high-band part coded information input from demultiplexing section  901  into optimum pitch coefficient T′, which is filtering related information, and a post-coding variation V q (j) index, which is gain related information. Then demultiplexing section  921  outputs optimum pitch coefficient T′ to filtering section  923 , and outputs the post-coding variation V q (j) index to gain decoding section  924 . If demultiplexing into optimum pitch coefficient T′ and a post-coding variation V q (j) index has been performed in demultiplexing section  901 , demultiplexing section  921  need not be provided. 
     Based on band setting information Band_Setting input from demultiplexing section  901 , filter state setting section  922  sets low-band part decoded spectrum S 1 ( k ) input from low-band decoding section  902  as a filter state used by filtering section  923 . Here, if an entire frequency band 0≦k&lt;Fmax spectrum in filtering section  923  is called S(k) for convenience, of spectrum S(k), low-band part decoded spectrum S 1 ( k ) is stored in a low-band part ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 )) band indicated by band setting information Band_Setting as a filter internal state (filter state). The configuration and operation of filter state setting section  922  are similar to those of filter state setting section  502  shown in  FIG. 5 , and therefore a detailed description thereof is omitted here. 
     Filtering section  923  is provided with a multi-tap pitch filter (that is, the number of taps is greater than 1). Filtering section  923  filters low-band part decoded spectrum S 1 ( k ) based on a filter state set by filter state setting section  922 , pitch coefficient T′ input from demultiplexing section  921 , a filter coefficient stored internally beforehand, and band setting information Band_Setting input from demultiplexing section  901 . Then filtering section  923  calculates estimated spectrum S′(k) of input spectrum S(k) as shown in equation 18 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       S 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           - 
                           1 
                         
                       
                       1 
                     
                     ⁢ 
                     
                       
                         
                           β 
                           i 
                         
                         · 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                         
                           ( 
                           
                             k 
                             - 
                             T 
                             + 
                             i 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   18 
                   ] 
                 
               
             
           
         
       
     
     The transfer function shown in equation 13 above is also used by filtering section  923 . Filtering section  923  outputs estimated spectrum S′(k) obtained by filtering to spectrum adjustment section  925 . 
     Gain decoding section  924  decodes a post-coding variation V q (j) index input from demultiplexing section  921  based on band setting information Band_Setting input from demultiplexing section  901 , and finds post-coding variation V q (j), which is a variation V(j) quantization value. Here, the gain codebook used for post-coding variation V q (j) index decoding is incorporated in gain decoding section  924 , and is similar to the gain codebook used by gain coding section  506  shown in  FIG. 5 . Gain decoding section  924  outputs post-coding variation V q (j) obtained by decoding to spectrum adjustment section  925 . 
     Spectrum adjustment section  925  multiplies estimated spectrum S′(k) input from filtering section  923  by post-coding variation V q (j) of each subband input from gain decoding section  924  for a high-band part specified by band setting information Band_Setting input from demultiplexing section  901  in accordance with equation 19 below. By this means, spectrum adjustment section  925  adjusts the spectrum shape in a high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) of estimated spectrum S′(k), generates decoded spectrum S 2 ( k ), and outputs this to orthogonal transform processing section  802 . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           S 
                           ′ 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       · 
                       
                         
                           V 
                           q 
                         
                         ⁡ 
                         
                           ( 
                           j 
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             
                               Max 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             ≤ 
                             k 
                             &lt; 
                             
                               F 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               max 
                             
                           
                         
                         
                           
                             
                               or 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               Max 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             ≤ 
                             k 
                             &lt; 
                             
                               F 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               max 
                             
                           
                         
                       
                       
                         
                           
                             
                               j 
                               = 
                               0 
                             
                             , 
                             … 
                             ⁢ 
                             
                                 
                             
                             , 
                             
                               J 
                               - 
                               1 
                             
                           
                         
                         
                           
                               
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   19 
                   ] 
                 
               
             
           
         
       
     
     In equation 19, j indicates a subband index when gain is encoded, and is set according to spectrum index k. That is to say, for spectrum index k included in a subband for which the subband index is j″, estimated spectrum S′(k) is multiplied by V q (j″). 
     Here, a low-band part ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 )) of decoded spectrum S 2 ( k ) comprises first layer decoded spectrum S 1 ( k ), and a high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax)) of decoded spectrum S 2 ( k ) comprises post-spectrum-shape-adjustment estimated spectrum S′(k). 
     The actual processing performed by orthogonal transform processing section  802  will now be described. 
     Orthogonal transform processing section  802  has internal buffers buf 2 ( k ), which are initialized as shown in equation 20 below.
 
[20]
 
buf2( k )=0( k= 0, . . . ,N− 1)  (Equation 20)
 
     Also, orthogonal transform processing section  802  finds decoded signal y n  in accordance with equation 21 below using decoded spectrum S 2 ( k ) input from spectrum adjustment section  925 , and outputs decoded signal y n . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       n 
                     
                     = 
                     
                       
                         2 
                         N 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             
                               2 
                               ⁢ 
                               N 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Z 
                           ⁢ 
                           
                             ( 
                             k 
                             ) 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         k 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   π 
                                 
                                 
                                   4 
                                   ⁢ 
                                   N 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         n 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         N 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   21 
                   ] 
                 
               
             
           
         
       
     
     In equation 21, Z(k) is a vector that links decoded spectrum S 2 ( k ) and buffer buf 2 ( k ) as shown in equation 22 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Z 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             buf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 k 
                                 = 
                                 0 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 k 
                                 = 
                                 N 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   22 
                   ] 
                 
               
             
           
         
       
     
     Next, orthogonal transform processing section  802  updates buffer buf 2 ( k ) in accordance with equation 23 below.
 
[23]
 
buf2( k )= S 2( k )( k= 0, . . . , N− 1)  (Equation 23)
 
     Orthogonal transform processing section  802  then outputs decoded signal y n  as an output signal. 
     This concludes a description of the internal configuration of decoding apparatus  103 . 
     Thus, according to this embodiment, in a coding/decoding method that performs band enhancement using a low-band part spectrum and generates/estimates a high-band part spectrum, an encoding apparatus/decoding apparatus decides band setting—that is, which bands a low-band part and high-band part are—adaptively according to an input signal characteristic. By this means, high-band part spectral data such as a wideband signal or an ultrawideband signal can be encoded efficiently, and the quality of a decoded signal can be improved. 
     Specifically, band setting section  301  compares low-band part energy and high-band part energy of input signal spectral data, and if the low-band part energy is significantly greater than the high-band part energy, sets a narrower low-band part and a wider high-band part. By this means, low-band part spectral data that greatly influences the quality of a decoded signal when an input signal is speech can be encoded intensively by means of a shape-gain coding method, and the quality of a decoded signal can be increased. On the other hand, if low-band part energy is not that much greater than high-band part energy, band setting section  301  sets a wider low-band part and a narrower high-band part. By this means, encoding distortion can be reduced with a shape-gain coding method up to a higher band part, and bandwidth limitation that greatly influences the quality of a decoded signal when an input signal is audio can be improved. 
     In this embodiment, a configuration has been described whereby division into different subband configurations is performed by band division section  501  and gain coding section  506  in high-band coding section  303 , but the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby division is performed into identical subband configurations. 
     In this embodiment, a configuration has been described whereby a high-band part spectrum is divided into P parts by band division section  501  in high-band coding section  303  irrespective of the value of band setting information Band_Setting. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby a subband is divided into different numbers according to the value of band setting information Band_Setting. For example, when band setting information Band_Setting is 0, a high-band part spectrum bandwidth is wider than when band setting information Band_Setting is 1, and therefore in this case division is performed into a number greater than P. By this means, it is possible to prevent degradation of coding performance due to a subband width being too great. 
     Also, in this embodiment, a configuration has been described whereby an input spectrum low-band part is set as a filter state in high-band coding section  303 , and a search is performed for a spectrum position that is similar to an input spectrum high-band part. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby a search is performed for a spectrum position that is similar to an input spectrum high-band part for a low-band part decoded spectrum obtained by decoding low-band part coded information output from a low-band coding section. When the above configuration is employed, a low-band part decoded spectrum obtained on the decoding apparatus side can also be used, enabling operation on the decoding apparatus side to be ensured. 
     Also, when the above configuration is employed, it is necessary for a low-band part decoding section that performs local decoding for calculating a low-band part decoded spectrum to be newly provided in coding section  202 , and for a low-band part decoded spectrum to be output from the low-band decoding section to high-band coding section  303 . 
     Embodiment 2 
     Embodiment 2 describes a configuration in which a first layer coding section that encodes a low-band part of spectral data is newly provided, and the coding method described in Embodiment 1 is applied to difference data between input signal spectral data and a first layer coding section coding result. Below, a coding layer in which the coding method described in Embodiment 1 is applied is described as a second layer coding section. 
     A communication system according to Embodiment 2 (not shown) is basically similar to the communication system shown in  FIG. 1 , and differs from encoding apparatus  101  and decoding apparatus  103  of the communication system in  FIG. 1  only in parts of the configuration and operation of the encoding apparatus and decoding apparatus. In the following description, reference codes “ 111 ” and “ 113 ” are assigned respectively to an encoding apparatus and decoding apparatus of a communication system according to this embodiment. 
       FIG. 12  is a block diagram showing the internal principal-part configuration of encoding apparatus  111  according to this embodiment. Encoding apparatus  111  according to this embodiment mainly comprises down-sampling processing section  1001 , first layer coding section  1002 , first layer decoding section  1003 , up-sampling processing section  1004 , orthogonal transform processing section  1005 , second layer coding section  1006 , and coded information integration section  1007 . These sections perform the following operations. 
     If the sampling frequency of input signal x n  is designated SR input , down-sampling processing section  1001  performs down-sampling of input signal sampling frequency from SR Input  to SR base  (where SR base &lt;SR input ), and outputs a down-sampled input signal to first layer coding section  1002  as a post-down-sampling input signal. 
     First layer coding section  1002  performs encoding on a post-down-sampling input signal input from down-sampling processing section  1001  using, for example, a CELP (Code Excited Linear Prediction) type speech coding method, and generates first layer coded information. Then first layer coding section  1002  outputs the generated first layer coded information to first layer decoding section  1003  and coded information integration section  1007 . 
     First layer decoding section  1003  performs decoding on first layer coded information input from first layer coding section  1002  using, for example, a CELP speech decoding method, and generates a first layer decoded signal. Then first layer decoding section  1003  outputs the generated first layer decoded signal to up-sampling processing section  1004 . 
     Up-sampling processing section  1004  performs up-sampling of the sampling frequency of a first layer decoded signal input from first layer decoding section  1003  from SR base  to SR input . Then up-sampling processing section  1004  outputs an up-sampled first layer decoded signal to orthogonal transform processing section  1005  as post-up-sampling first layer decoded signal c 1   n . 
     Orthogonal transform processing section  1005  has internal buffers buf 1   n  and buf 2   n  (n=0, . . . , N−1). Orthogonal transform processing section  1005  performs a Modified Discrete Cosine Transform (MDCT) on input signal x n  and post-up-sampling first layer decoded signal c 1   n  input from up-sampling processing section  1004 . Orthogonal transform processing section  1005  performs orthogonal transform processing of input signal x n  and post-up-sampling first layer decoded signal c 1   n , and calculates input spectrum X(k) and first layer decoded spectrum C(k). The processing performed by orthogonal transform processing section  1005  is similar to the processing described in Embodiment 1, and therefore a description thereof is omitted here. Orthogonal transform processing section  1005  outputs obtained input spectrum X(k) and first layer decoded spectrum C(k) to second layer coding section  1006 . 
     Second layer coding section  1006  generates second layer coded information using input spectrum X(k) and first layer decoded spectrum C(k) input from orthogonal transform processing section  1005 , and outputs the generated second layer coded information to coded information integration section  1007 . Details of second layer coding section  1006  will be given later herein. 
     Coded information integration section  1007  integrates first layer coded information input from first layer coding section  1002  and second layer coded information input from second layer coding section  1006 . Then coded information integration section  1007  adds a transmission error code or the like to the integrated information source code if necessary, and then outputs this to channel  102  as coded information. 
     The internal principal-part configuration of second layer coding section  1006  shown in  FIG. 12  will now be described with reference to  FIG. 13 . 
     Second layer coding section  1006  mainly comprises band setting section  1101 , low-band coding section  1102 , high-band coding section (band enhancement section)  1103 , and multiplexing section  1104 . 
     Input spectrum X(k) and first layer decoded spectrum C(k) are input to band setting section  1101  from orthogonal transform processing section  1005 . Band setting section  1101  analyzes the spectral characteristics of input spectrum X(k) and first layer decoded spectrum C(k), and sets bands subject to coding by low-band coding section  1102  and high-band coding section (band enhancement section)  1103  respectively according to the analysis results. Then band setting section  1101  outputs this information as band setting information to low-band coding section  1102 , high-band coding section  1103 , and multiplexing section  1104 . 
     The band setting information calculation method used by band setting section  1101  will now be described. 
     Band setting section  1101  first calculates difference spectrum C sub (k) between input spectrum X(k) and first layer decoded spectrum C(k) by means of equation 24. In equation 24, Fmax is the maximum band value (maximum frequency value).
 
[24]
 
 C   sub ( k )= X ( k )− S 1( k )( k= 0, . . . , F max)  (Equation 24)
 
     Then band setting section  1101  calculates, for difference spectrum C sub (k), energy (low-band energy) E Low  of a part for which the band is less than or equal to TH Low  in accordance with equation 25-1, and energy (high-band energy) E High  of a part for which the band is greater than or equal to TH High  in accordance with equation 25-2, where TH Low  and TH High  are predetermined threshold values, and TH Low &lt;TH High . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     25 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     Low 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       
                         TH 
                         Low 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           C 
                           sub 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   25 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     25 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     High 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         
                           TH 
                           High 
                         
                       
                       Fmax 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           C 
                           sub 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Next, band setting section  1101  compares the magnitude of low-band energy E Low  and the magnitude of high-band energy E High  calculated by means of equations 25, and decides band setting information Band_Setting in accordance with equation 26. Here, γ in equation 26 is a predetermined constant. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Band_Setting 
                   = 
                   
                     { 
                     
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 if 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   E 
                                   Low 
                                 
                               
                               ≥ 
                               
                                 γ 
                                 · 
                                 
                                   E 
                                   High 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           1 
                         
                         
                           
                             ( 
                             else 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   26 
                   ] 
                 
               
             
           
         
       
     
     That is to say, band setting section  1101  sets the band setting information Band_Setting value to 0 if low-band energy E Low  is somewhat greater than high-band energy E High , and sets the band setting information Band_Setting value to 1 otherwise. Band setting section  1101  outputs decided band setting information Band_Setting to low-band coding section  1102 , high-band coding section  1103 , and multiplexing section  1104 . 
     Input spectrum X(k) and first layer decoded spectrum C(k) are input to low-band coding section  1102  from orthogonal transform processing section  1005 . Also, band setting information Band_Setting is input to low-band coding section  1102  from band setting section  1101 . Based on band setting information Band_Setting, low-band coding section  1102  encodes difference spectrum C sub (k) between input spectrum X(k) and first layer decoded spectrum C(k), and generates low-band part coded information. Then low-band coding section  1102  outputs the low-band part coded information to multiplexing section  1104 . Details of the processing performed by low-band coding section  1102  will be given later herein. 
     Input spectrum X(k) and first layer decoded spectrum C(k) are input to high-band coding section  1103  from orthogonal transform processing section  1005 . Also, band setting information Band_Setting is input to high-band coding section  1103  from band setting section  1101 . Based on band setting information Band_Setting, high-band coding section  1103  encodes input spectrum X(k) and generates high-band part coded information (band enhancement information). Then, high-band coding section  1103  outputs the high-band part coded information to multiplexing section  1104 . Details of the processing performed by high-band coding section  1103  will be given later herein. 
     Multiplexing section  1104  multiplexes band setting information Band_Setting, low-band part coded information, and high-band part coded information input from band setting section  1101 , low-band coding section  1102 , and high-band coding section  1103  respectively, and generates second layer coded information. Then multiplexing section  1104  outputs the obtained second layer coded information to coded information integration section  1007 . Band setting information, low-band part coded information, and high-band part coded information may also be input directly to coded information integration section  1007 , and multiplexed by coded information integration section  1007 . 
       FIG. 14  is a block diagram showing the internal configuration of low-band coding section  1102 . Low-band coding section  1102  mainly comprises difference spectrum calculation section  1201 , shape coding section  1202 , gain coding section  1203 , and multiplexing section  1204 . These sections perform the following operations. 
     Difference spectrum calculation section  1201  calculates difference spectrum C sub (k) between input spectrum X(k) and first layer decoded spectrum C(k), and outputs calculated difference spectrum C sub (k) to shape coding section  1202 . 
     Difference spectrum C sub (k) is input to shape coding section  1202  from difference spectrum calculation section  1201 . Shape coding section  1202  encodes difference spectrum C sub (k) shape information, and outputs this to multiplexing section  1204  as shape coded information. Also, shape coding section  1202  calculates an ideal gain at the time of shape information coding, and outputs the calculated ideal gain to gain coding section  1203 . The processing performed by shape coding section  1202  is similar to that of shape coding section  402  shown in  FIG. 4 , and therefore a description thereof is omitted here. 
     Ideal gain is input to gain coding section  1203  from shape coding section  1202 . Gain coding section  1203  encodes the ideal gain, and outputs this to multiplexing section  1204  as gain coded information. The processing performed by gain coding section  1203  is similar to that of gain coding section  403  shown in  FIG. 4 , and therefore a description thereof is omitted here. 
       FIG. 15  is a block diagram showing the internal configuration of high-band coding section  1103 . High-band coding section  1103  is provided with band division section  1301 , filter state setting section  1302 , filtering section  1303 , search section  1305 , pitch coefficient setting section  1304 , gain coding section  1306 , and multiplexing section  1307 , which perform the operations described below. With the exception of filter state setting section  1302 , the above configuration elements perform similar processing to that of identically named configuration elements shown in  FIG. 5 , and therefore descriptions thereof are omitted here. 
     Filter state setting section  1302  sets first layer decoded spectrum C(k) input from orthogonal transform processing section  1005  as a filter state used by filtering section  1303 . First layer decoded spectrum C(k) is stored as a filter internal state (filter state) in an entire frequency band 0≦k&lt;Fmax spectrum S(k) ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 )) band in filtering section  1303 . 
     This concludes a description of the processing performed by high-band coding section  1103 . 
     This concludes a description of the configuration of encoding apparatus  111 . 
     Decoding apparatus  113  according to this embodiment will now be described. 
       FIG. 16  is a block diagram showing the internal principal-part configuration of decoding apparatus  113 . Decoding apparatus  113  mainly comprises coded information demultiplexing section  1401 , first layer decoding section  1402 , up-sampling processing section  1403 , orthogonal transform processing section  1404 , second layer decoding section  1405 , and orthogonal transform processing section  1406 . These sections perform the following operations. 
     Coded information transmitted from encoding apparatus  111  via channel  102  is input to coded information demultiplexing section  1401 . Coded information demultiplexing section  1401  demultiplexes the input coded information into first layer coded information and second layer coded information, outputs the first layer coded information to first layer decoding section  1402 , and outputs the second layer coded information to second layer decoding section  1405 . 
     First layer decoding section  1402  decodes the first layer coded information input from coded information demultiplexing section  1401  and generates a first layer decoded signal, and outputs the generated first layer decoded signal to up-sampling processing section  1403 . The operation of first layer decoding section  1402  is similar to that of first layer decoding section  1003  shown in  FIG. 12 , and therefore a detailed description thereof is omitted here. 
     Up-sampling processing section  1403  performs up-sampling of the sampling frequency of a first layer decoded signal input from first layer decoding section  1402  from SR base  to SR input , and outputs an obtained post-up-sampling first layer decoded signal to orthogonal transform processing section  1404 . 
     Orthogonal transform processing section  1404  performs orthogonal transform processing (MDCT) on a post-up-sampling first layer decoded signal input from up-sampling processing section  1403 . Then orthogonal transform processing section  1404  outputs obtained post-up-sampling first layer decoded signal MDCT coefficient (hereinafter referred to as first layer decoded spectrum) C(k) to second layer decoding section  1405 . The operation of orthogonal transform processing section  1404  is similar to the processing on a post-up-sampling first layer decoded signal by orthogonal transform processing section  1005  shown in  FIG. 12 , and therefore a detailed description thereof is omitted here. 
     Second layer decoding section  1405  generates second layer decoded spectrum S 2 ( k ) including a high-band component using first layer decoded spectrum C(k) input from orthogonal transform processing section  1404  and second layer coded information input from coded information demultiplexing section  1401 . Then second layer decoding section  1405  outputs generated second layer decoded spectrum S 2 ( k ) to orthogonal transform processing section  1406 . Details of the processing performed by second layer decoding section  1405  will be given later herein. 
     Orthogonal transform processing section  1406  executes an orthogonal transform on second layer decoded spectrum S 2 ( k ) input from second layer decoding section  1405 , and converts it to a time-domain signal. Orthogonal transform processing section  1406  outputs the obtained signal as an output signal. The operation of orthogonal transform processing section  1406  is similar to the processing by orthogonal transform processing section  802  shown in  FIG. 8 , and therefore a detailed description thereof is omitted here. 
       FIG. 17  is a block diagram showing the internal configuration of second layer decoding section  1405  shown in  FIG. 16 . Second layer decoding section  1405  mainly comprises demultiplexing section  1501 , low-band decoding section  1502 , high-band decoding section (band enhancement section)  1503 , and spectrum synthesis section  1504 . 
     Second layer coded information is input to demultiplexing section  1501  from coded information demultiplexing section  1401 . Demultiplexing section  1501  demultiplexer the coded information into low-band part coded information, high-band part coded information, and band setting information. Then demultiplexing section  1501  outputs the low-band part coded information to low-band decoding section  1502 , outputs the high-band part coded information (band enhancement information) to high-band decoding section  1503 , and outputs the band setting information to low-band decoding section  1502  and high-band decoding section  1503 . 
     Low-band part coded information and band setting information are input to low-band decoding section  1502  from demultiplexing section  1501 . Low-band decoding section  1502  generates a low-band part decoded spectrum from the input low-band part coded information and band setting information, and outputs the generated low-band part decoded spectrum to spectrum synthesis section  1504 . The processing performed by low-band decoding section  1502  is similar to that of low-band decoding section  902  shown in  FIG. 10 , and therefore a description thereof is omitted here. 
     High-band part coded information and band setting information are input to high-band decoding section  1503  from demultiplexing section  1501 . First layer decoded spectrum C(k) is input to high-band decoding section  1503  from orthogonal transform processing section  1404 . High-band decoding section  1503  generates a high-band part decoded spectrum from input first layer decoded spectrum C(k) and high-band part coded information, and outputs the generated high-band part decoded spectrum to spectrum synthesis section  1504 . 
       FIG. 18  is a block diagram showing the internal configuration of high-band decoding section  1503 . High-band decoding section  1503  mainly comprises demultiplexing section  1601 , filter state setting section  1602 , filtering section  1603 , gain decoding section  1604 , and spectrum adjustment section  1605 , which perform the operations described below. With the exception of filter state setting section  1602 , the above configuration elements perform similar processing to that of identically named configuration elements shown in  FIG. 11 , and therefore descriptions thereof are omitted here. 
     Based on band setting information Band_Setting input from demultiplexing section  1501 , filter state setting section  1602  sets first layer decoded spectrum C(k) input from orthogonal transform processing section  1404  as a filter state used by filtering section  1603 . Here, an entire frequency band 0≦k&lt;Fmax spectrum in filtering section  1603  is called S(k) for convenience. In this case, of spectrum S(k), first layer decoded spectrum C(k) is stored in a low-band part ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 )) band indicated by band setting information Band_Setting as a filter internal state (filter state). The configuration and operation of filter state setting section  1602  are similar to those of filter state setting section  502  shown in  FIG. 5 , and therefore a detailed description thereof is omitted here. 
     This concludes a description of the processing performed by high-band decoding section  1503 . 
     Low-band part decoded spectrum S 1 ( k ) is input to spectrum synthesis section  1504  from low-band decoding section  1502 . Also, high-band part decoded spectrum S 2 ( k ) is input to spectrum synthesis section  1504  from high-band decoding section  1503 . Spectrum synthesis section  1504  adds input low-band part decoded spectrum S 1 ( k ) and high-band part decoded spectrum S 2 ( k ) in the frequency domain by means of equation 27, and calculates addition spectrum S add (k). Spectrum synthesis section  1504  outputs calculated addition spectrum S add (k) to orthogonal transform processing section  1406 .
 
[27]
 
 S   add ( k )= S 1( k )+ S 2( k )( k= 0, . . . , F max)  (Equation 27)
 
     This concludes a description of the internal configuration of decoding apparatus  113 . 
     Thus, according to this embodiment, even in a configuration using a coding/decoding method that performs band enhancement using a low-band part spectrum and generates/estimates a high-band part spectrum, and in which there is a coding layer (core layer) that encodes a low band, an encoding apparatus/decoding apparatus decides band setting—that is, which bands a low-band part and high-band part are—adaptively according to an input signal characteristic. By this means, high-band part spectral data such as a wideband signal or an ultrawideband signal can be encoded efficiently, and the quality of a decoded signal can be improved. 
     Specifically, band setting section  1101  compares low-band part energy and high-band part energy of difference data between input signal spectral data and spectral data encoded by the core layer. Then, if the low-band part energy is significantly greater than the high-band part energy, band setting section  1101  sets a narrower low-band part narrower and a wider high-band part. By this means, low-band part spectral data that greatly influences the quality of a decoded signal when an input signal is speech can be encoded intensively by means of a shape-gain coding method, and the quality of a decoded signal can be increased. Also, if low-band part energy is not that much greater than high-band part energy, band setting section  1101  sets a wider low-band part and a narrower high-band part. By this means, coding distortion can be reduced with a shape-gain coding method up to a higher band part, and bandwidth limitation that greatly influences the quality of a decoded signal when an input signal is audio can be improved. 
     In this embodiment, band setting section  1101  decides band setting information Band_Setting based on an energy ratio of a low-band part and high-band part of a difference spectrum between an input spectrum and first layer decoded spectrum. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby band setting section  1101  decides band setting information Band_Setting based on an energy ratio of a low-band part and high-band part of an input spectrum. 
     Also, a configuration has been described whereby a first layer decoded spectrum is set as a filter state in high-band decoding section  1503  in a decoding apparatus according to this embodiment. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby a low-band part of a spectrum obtained by adding a first layer decoded spectrum and low-band part decoded spectrum in the frequency domain is set as a filter state. By this means, a low-band part spectrum used in band enhancement is more similar to an input spectrum, so that the precision of a low-band part used in band enhancement is improved, and as a result, the quality of a decoded signal can be further improved. In the above configuration, it is necessary for a low-band part decoded spectrum to be output to high-band decoding section  1503  from low-band decoding section  1502 . 
     Embodiment 3 
     In Embodiment 3 of the present invention, a configuration is described in which a first layer coding section that encodes a low-band part of spectral data is newly provided in the same way as in Embodiment 2, and the coding method described in Embodiment 1 is applied to difference data between input signal spectral data and a first layer coding section coding result. Below, a coding layer in which the coding method described in Embodiment 1 is applied is described as a second layer coding section. However, in this embodiment, a configuration is described whereby a band other than a band encoded by the first layer coding section is encoded by the second layer coding section. That is to say, a second layer coding section of Embodiment 2 has a configuration in which only a high-band coding section (band enhancement section) is present. 
     A communication system according to Embodiment 3 (not shown) is basically similar to the communication system shown in  FIG. 1 , and differs from encoding apparatus  101  and decoding apparatus  103  of the communication system in  FIG. 1  only in parts of the configuration and operation of the encoding apparatus and decoding apparatus. In the following description, reference codes “ 121 ” and “ 123 ” are assigned respectively to an encoding apparatus and decoding apparatus of a communication system according to this embodiment. 
     Encoding Apparatus  121   
       FIG. 19  is a block diagram showing the internal principal-part configuration of encoding apparatus  121  according to this embodiment. Encoding apparatus  121  according to this embodiment mainly comprises down-sampling processing section  1001 , first layer coding section  1002 , first layer decoding section  1003 , up-sampling processing section  1004 , orthogonal transform processing section  1005 , second layer coding section  1701 , and coded information integration section  1007 . These sections perform the following operations. With the exception of second layer coding section  1701 , the above configuration elements perform the same processing as configuration elements in encoding apparatus  111  described in Embodiment 2, and are therefore assigned the same reference codes, and descriptions thereof are omitted here. 
     Second layer coding section  1701  generates second layer coded information using input spectrum X(k) and first layer decoded spectrum C(k) input from orthogonal transform processing section  1005 , and outputs the generated second layer coded information to coded information integration section  1007 . 
     The internal principal-part configuration of second layer coding section  1701  shown in  FIG. 19  will now be described with reference to  FIG. 20 . 
     Second layer coding section  1701  mainly comprises band setting section  1801 , high-band coding section (band enhancement section)  1802 , and multiplexing section  1803 . These sections perform the following operations. 
     Input spectrum X(k) and first layer decoded spectrum C(k) are input to band setting section  1801  from orthogonal transform processing section  1005 . Band setting section  1801  analyzes the spectral characteristics of input spectrum X(k) and first layer decoded spectrum C(k). Band setting section  1801  sets a band subject to coding by high-band coding section (band enhancement section)  1802  according to the analysis results, and outputs this as band setting information to high-band coding section  1802  and multiplexing section  1803 . 
     The band setting information calculation method used by band setting section  1801  will now be described. 
     Band setting section  1801  first calculates difference spectrum C sub (k) between input spectrum X(k) and first layer decoded spectrum C(k) by means of equation 28. In equation 28, Fmax is the maximum band value (maximum frequency value).
 
 C   sub ( k )= X ( k )− C ( k )=0, . . .  F max)  (Equation 28)
 
     Then band setting section  1801  calculates, for difference spectrum C sub (k), energy (first band energy) E 1  of a part for which the band is TH 1   Low  to TH 1   High  and energy (second band energy) E 2  of a part for which the band is TH 2   Low  to TH 2   High  in accordance with equations 29-1 and 29-2. Here, TH 1   Low , TH 1   High , TH 2   Low , and TH 2   High  are predetermined threshold values, TH 1   Low &lt;TH 2   Low , and TH 1   High &lt;TH 2   High . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     29 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     1 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         
                           TH 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             1 
                             Low 
                           
                         
                       
                       
                         TH 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           1 
                           High 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           C 
                           sub 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   29 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     29 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     E 
                     2 
                   
                   = 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         
                           TH 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             2 
                             Low 
                           
                         
                       
                       
                         TH 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           High 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           C 
                           sub 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Next, band setting section  1801  compares the magnitude of first band energy E 1  calculated by means of equation 29-1 and the magnitude of second band energy E 2  calculated by means of equation 29-2, and decides band setting information Band_Setting in accordance with equation 30. Here, γ 2  in equation 30 is a predetermined constant. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   Band_Setting 
                   = 
                   
                     { 
                     
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 if 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   E 
                                   1 
                                 
                               
                               ≥ 
                               
                                 γ2 
                                 · 
                                 
                                   E 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           1 
                         
                         
                           
                             ( 
                             else 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   30 
                   ] 
                 
               
             
           
         
       
     
     That is to say, band setting section  1801  sets the band setting information Band_Setting value to 0 if first band energy E 1  is somewhat greater than second band energy E 2 , and sets the band setting information Band_Setting value to 1 otherwise. Band setting section  1801  outputs decided band setting information Band_Setting to high-band coding section  1802  and multiplexing section  1803 . 
     Input spectrum X(k) and first layer decoded spectrum C(k) are input to high-band coding section  1802  from orthogonal transform processing section  1005 . Also, band setting information Band_Setting is input to high-band coding section  1802  from band setting section  1801 . Based on band setting information Band_Setting, high-band coding section  1802  encodes input spectrum X(k) and generates high-band part coded information (band enhancement information). Then high-band coding section  1802  outputs the high-band part coded information to multiplexing section  1803 . Details of the processing performed by high-band coding section  1802  will be given later herein. 
     Multiplexing section  1803  multiplexes band setting information and high-band part coded information input from band setting section  1801  and high-band coding section  1802  respectively, and outputs the multiplexed information to coded information integration section  1007  as second layer coded information. Band setting information and high-band part coded information may also be input directly to coded information integration section  1007 , and multiplexed by coded information integration section  1007 . 
       FIG. 21  is a block diagram showing the internal configuration of high-band coding section  1802 . High-band coding section  1802  is provided with band division section  1311 , filter state setting section  1302 , filtering section  1303 , search section  1305 , pitch coefficient setting section  1304 , gain coding section  1306 , and multiplexing section  1307 , which perform the operations described below. With the exception of band division section  1311 , the above configuration elements perform the same processing as configuration elements shown in  FIG. 15 , and are therefore assigned the same reference codes, and descriptions thereof are omitted here. 
     Input spectrum X(k) is input to band division section  1311  from orthogonal transform processing section  1005 . Also, band setting information Band_Setting is input to band division section  1311  from band setting section  1801 . Band division section  1311  divides a high-band part of input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1) according to the band setting information Band_Setting value. Band division section  1311  outputs bandwidth BW p  (p=0, 1, . . . , P−1) and initial index BS p  (p=0, 1, . . . , P−1) of each subband to filtering section  1303 , search section  1305 , and multiplexing section  1307  as band division information. 
     Specifically, if the band setting information Band_Setting value is 0, band division section  1311  divides a part for which the band is less than or equal to Max 3  (Flow≦k&lt;Max 3 ) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). Also, if the band setting information Band_Setting value is 1, band division section  1311  divides a part for which the band is less than or equal to Max 4  (Flow≦k&lt;Max 4 ) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). Here, Max 3  and Max 4  are predetermined constants, and Max 3 &lt;Max 4 . Also, Flow is a maximum frequency band value corresponding to a sampling frequency of a signal down-sampled by down-sampling processing section  1001 . That is to say, it is the maximum usable frequency index of a first layer decoded spectrum. Also, below, a part in subband SB p  within input spectrum X(k) is denoted as subband spectrum X p (k) (BS p ≦k&lt;BS p +BW p ). 
     The effect of the above-described kind of band division method will now be described. Band setting information Band_Setting is set by comparing energy (first band energy) E 1  of a part for which the band is TH 1   Low  to TH 1   High  and energy (second band energy) E 2  of a part for which the band is TH 2   Low  to TH 2   High . If this band setting information Band_Setting value is 0, this means that low-band side energy is greater than high-band side energy. In this case, a band encoded by high-band coding section  1802  is given a narrow setting (Flow≦k&lt;Max 3 ) by band division section  1311 , and there is an effect of improving the quality of a decoded signal by focusing coding on a lower band with high energy. Also, if the band setting information Band_Setting value is 1, this means that high-band side energy is greater than low-band side energy. In this case, a band encoded by high-band coding section  1802  is given a wider and higher-band setting (Flow≦k&lt;Max 4 ) by band division section  1311 , and there is an effect of improving the quality of a decoded signal by performing encoding up to a band on the high-band side with high energy. 
     This concludes a description of the processing performed by high-band coding section  1802 . 
     This concludes a description of the configuration of encoding apparatus  121 . 
     Decoding apparatus  123  according to this embodiment will now be described. 
       FIG. 22  is a block diagram showing the internal principal-part configuration of decoding apparatus  123 . Decoding apparatus  123  mainly comprises coded information demultiplexing section  1401 , first layer decoding section  1402 , up-sampling processing section  1403 , orthogonal transform processing section  1404 , second layer decoding section  1901 , and orthogonal transform processing section  1406 . With the exception of second layer decoding section  1901 , the above configuration elements perform the same processing as configuration elements in decoding apparatus  113  of Embodiment 2, and are therefore assigned the same reference codes, and descriptions thereof are omitted here. 
     Second layer decoding section  1901  generates second layer decoded spectrum S 2 ( k ) including a high-band component using first layer decoded spectrum C(k) input from orthogonal transform processing section  1404  and second layer coded information input from coded information demultiplexing section  1401 . Second layer decoding section  1901  outputs generated second layer decoded spectrum S 2 ( k ) to orthogonal transform processing section  1406 . 
       FIG. 23  is a block diagram showing the internal configuration of second layer decoding section  1901  shown in  FIG. 22 . Second layer decoding section  1901  mainly comprises demultiplexing section  2001  and high-band decoding section (band enhancement section)  2002 . 
     Second layer coded information is input to demultiplexing section  2001  from coded information demultiplexing section  1401 . Demultiplexing section  2001  demultiplexes the coded information into high-band part coded information and band setting information, and outputs these to high-band decoding section  2002 . 
     High-band part coded information and band setting information are input to high-band decoding section  2002  from demultiplexing section  2001 . High-band decoding section  2002  generates a decoded spectrum from the input high-band part coded information and band setting information, and outputs the generated decoded spectrum to orthogonal transform processing section  1406 . 
     Apart from input information being a first layer decoded spectrum rather than a low-band part decoded spectrum, the processing performed by high-band decoding section  2002  is similar to that of high-band decoding section  903  shown in  FIG. 9 , and therefore a description thereof is omitted here. 
     This concludes a description of the internal configuration of decoding apparatus  123 . 
     Thus, according to this embodiment, even in a configuration using a coding/decoding method that performs band enhancement using a low-band part spectrum and generates/estimates a high-band part spectrum, and in which there is a coding layer (core layer) that encodes a low band, an encoding apparatus/decoding apparatus decides band setting to be enhanced—that is, a spectrum of up to which band is generated by means of band enhancement—adaptively according to an input signal characteristic. By this means, high-band part spectral data such as a wideband signal or an ultrawideband signal can be encoded efficiently, and the quality of a decoded signal can be improved. 
     Specifically, band setting section  1801  compares low-band part energy (first band energy) and high-band part energy (second band energy) of difference data between input signal spectral data and spectral data encoded by the core layer. Then, if the first band energy is significantly greater than the second band energy, band setting section  1801  makes a narrower setting for a high-band part generated by band enhancement. By this means, middle-band part spectral data that greatly influences the quality of a decoded signal when an input signal is speech can be encoded intensively, and the quality of a decoded signal can be increased. Here, a middle-band part denotes a band on the low-band side even within a high-band part when a band is divided into a low-band part and high-band part. Also, if first band energy is not that much greater than second band energy, band setting section  1801  makes a wider setting for a high-band part generated by band enhancement. By this means, bandwidth limitation that greatly influences the quality of a decoded signal when an input signal is audio can be improved by performing band enhancement up to a higher-band part. 
     In this embodiment, a configuration has been described by way of example in which band setting section  1801  adjusts the upper limit of a band of a spectrum generated by high-band coding section  1802 . However, the present invention is not limited to this, and can also be applied in a similar way to a configuration in which high-band coding section  1802  adjusts other than a band upper limit (for example, a band lower limit or the like) of a spectrum generated by high-band coding section  1802 . 
     As described above, according to this embodiment, when generating high-band part spectral data of a signal subject to coding based on low-band part spectral data, an encoding apparatus decides band setting—that is, which bands a low-band part and high-band part are—adaptively according to an input signal characteristic. By this means, high-band part spectral data such as a wideband signal or an ultrawideband signal can be encoded efficiently, and the quality of a decoded signal in a decoding apparatus can be improved. 
     Embodiment 4 
     With the band enhancement methods disclosed in Patent Literature 1 and Patent Literature 2, band setting is fixed irrespective of input signal characteristics such as described in Embodiment 1, Embodiment 2, and Embodiment 3. Here, an input signal characteristic is an energy ratio between a low-band spectrum and a high-band spectrum, tonality, or the like. Similarly, with the band enhancement methods disclosed in Patent Literature 1 and Patent Literature 2, band setting is fixed irrespective of conditions at the time of coding. 
     Band enhancement technology is essentially a technology that generates spectral data of a high-band part of a signal subject to coding in a pseudo fashion with very little information (very few bits) using a low-band part spectral data obtained by decoding high-band part spectral data. Consequently, if the coding bit rate is extremely high, using a spectrum coding method other than a band enhancement method will often enable the quality of a decoded signal to be improved. However, since the band enhancement methods disclosed in Patent Literature 1 and Patent Literature 2 always perform band enhancement using a fixed band setting irrespective of conditions at the time of coding, there is a problem of coding efficiency not being high. 
     In Embodiment 4 of the present invention, a configuration is described whereby band setting is switched adaptively in a band enhancement method according to conditions at the time of coding. Below, a case in which a coding bit rate is used as an example of conditions at the time of coding is taken by way of example. Here, a case is described by way of example in which three bit rates—BR 1 , BR 2 , and BR 3 —are used as coding bit rates. The relationship of the coding bit rates is assumed to be BR 1 &lt;BR 2 &lt;BR 3 . 
     A communication system according to Embodiment 4 (not shown) is basically similar to the communication system shown in  FIG. 1 , and differs from encoding apparatus  101  and decoding apparatus  103  of the communication system in  FIG. 1  only in parts of the configuration and operation of the encoding apparatus and decoding apparatus. In the following description, reference codes “ 131 ” and “ 133 ” are assigned respectively to an encoding apparatus and decoding apparatus of a communication system according to this embodiment. 
       FIG. 24  is a block diagram showing the internal principal-part configuration of encoding apparatus  131  according to this embodiment. Encoding apparatus  131  according to this embodiment mainly comprises down-sampling processing section  2401 , first layer coding section  2402 , first layer decoding section  2403 , up-sampling processing section  2404 , orthogonal transform processing section  2405 , second layer coding section  2406 , and coded information integration section  2407 . These sections perform the following operations. 
     If the sampling frequency of input signal x n  is designated SR input , down-sampling processing section  2401  performs input signal sampling frequency down-sampling from SR input  to SR base  (where SR base &lt;SR input ), and outputs a down-sampled input signal to first layer coding section  2402  as a post-down-sampling input signal. 
     First layer coding section  2402  performs coding on a post-down-sampling input signal input from down-sampling processing section  2401  using, for example, a CELP (Code Excited Linear Prediction) type speech coding method, and generates first layer coded information. Then first layer coding section  2402  outputs the generated first layer coded information to first layer decoding section  2403  and coded information integration section  2407 . 
     First layer decoding section  2403  performs decoding on first layer coded information input from first layer coding section  2402  using, for example, a CELP speech decoding method, and generates a first layer decoded signal. Then first layer decoding section  2403  outputs the generated first layer decoded signal to up-sampling processing section  2404 . 
     Up-sampling processing section  2404  performs up-sampling of the sampling frequency of a first layer decoded signal input from first layer decoding section  2403  from SR base  to SR input . Then up-sampling processing section  2404  outputs an up-sampled first layer decoded signal to orthogonal transform processing section  2405  as post-up-sampling first layer decoded signal c 1   n . 
     Orthogonal transform processing section  2405  has internal buffers buf 1   n  and buf 2   n  (n=0, . . . , N−1). Orthogonal transform processing section  2405  performs a Modified Discrete Cosine Transform (MDCT) on input signal x n  and post-up-sampling first layer decoded signal c 1   n  input from up-sampling processing section  2404 . Orthogonal transform processing section  2405  performs orthogonal transform processing of input signal x n  and post-up-sampling first layer decoded signal c 1   n , and calculates input spectrum X(k) and first layer decoded spectrum C 1 ( k ). The processing performed by orthogonal transform processing section  2405  is similar to the processing described in Embodiment 1, and therefore a description thereof is omitted here. Orthogonal transform processing section  2405  outputs obtained input spectrum X(k) and first layer decoded spectrum C 1 ( k ) to second layer coding section  2406 . 
     Second layer coding section  2406  generates second layer coded information using input spectrum X(k) and first layer decoded spectrum C 1 ( k ) input from orthogonal transform processing section  2405  based on coding bit rate information (hereinafter referred to as “bit rate information”) input to encoding apparatus  131  from outside, and outputs the generated second layer coded information to coded information integration section  2407 . Details of second layer coding section  2406  will be given later herein. In this embodiment, a case will be described by way of example in which encoding apparatus  131  uses three bit rates—BR 1 , BR 2 , and BR 3 —as coding bit rates, and the relationship of the coding bit rates is BR 1 &lt;BR 2 &lt;BR 3 . 
     Coded information integration section  2407  integrates first layer coded information input from first layer coding section  2402 , second layer coded information input from second layer coding section  2406 , and bit rate information. Then coded information integration section  2407  adds a transmission error code or the like to the integrated information source code if necessary, and then outputs this to channel  102  as coded information. 
     The internal principal-part configuration of second layer coding section  2406  shown in  FIG. 24  will now be described with reference to  FIG. 25 . 
     Second layer coding section  2406  mainly comprises band enhancement coding section  2501 , residual spectrum coding section  2502 , and multiplexing section  2503 . These sections perform the following operations. 
     First layer decoded spectrum C 1 ( k ) and input spectrum X(k) are input to band enhancement coding section  2501  from orthogonal transform processing section  2405 . Also, bit rate information is input to band enhancement coding section  2501  from outside. Furthermore, decoded residual spectrum D 1 ( k ) is input to band enhancement coding section  2501  from residual spectrum coding section  2502 . Band enhancement coding section  2501  calculates band enhancement coded information from input first layer decoded spectrum C 1 ( k ), input spectrum X(k), bit rate information, and decoded residual spectrum D 1 ( k ), and outputs this band enhancement coded information to multiplexing section  2503 . Details of the processing performed by band enhancement coding section  2501  will be given later herein. 
     First layer decoded spectrum C 1 ( k ) and input spectrum X(k) are input to residual spectrum coding section  2502  from orthogonal transform processing section  2405 . Also, bit rate information is input to residual spectrum coding section  2502  from outside. Residual spectrum coding section  2502  calculates residual spectrum coded information from input first layer decoded spectrum C 1 ( k ), input spectrum X(k), and bit rate information, and outputs this residual spectrum coded information to multiplexing section  2503 . Also, residual spectrum coding section  2502  outputs decoded residual spectrum D 1 ( k ) obtained by decoding the residual spectrum coded information to band enhancement coding section  2501 . Details of the processing performed by residual spectrum coding section  2502  and residual spectrum coded information will be given later herein. 
     Multiplexing section  2503  multiplexes band enhancement coded information and residual spectrum coded information input from band enhancement coding section  2501  and residual spectrum coding section  2502  respectively, and generates second layer coded information. Then multiplexing section  2503  outputs the obtained second layer coded information to coded information integration section  2407 . Band enhancement coded information and residual spectrum coded information may also be input directly to coded information integration section  2407 , and multiplexed by coded information integration section  2407 . 
       FIG. 26  is a block diagram showing the internal configuration of band enhancement coding section  2501 . Band enhancement coding section  2501  is provided with band division section  2601 , addition spectrum calculation section  2602 , filter state setting section  1302 , filtering section  1303 , search section  1305 , pitch coefficient setting section  1304 , gain coding section  1306 , and multiplexing section  1307 , which perform the operations described below. With the exception of band division section  2601  and addition spectrum calculation section  2602 , the above configuration elements perform similar processing to that of identically named configuration elements shown in  FIG. 15 , and therefore descriptions thereof are omitted here. However, for filter state setting section  1302  only, processing differs from that of the identically named configuration element shown in  FIG. 15  in terms of the name of an input spectrum and the input source configuration element name. 
     Input spectrum X(k) is input to band division section  2601  from orthogonal transform processing section  2405 . Also, bit rate information is input to band division section  2601  from outside. Band division section  2601  divides a high-band part of input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1) according to the bit rate information. 
     Specifically, if the bit rate information indicates that the coding bit rate is BR 1 , band division section  2601  divides a part for which the band is greater than or equal to Max 1  (Max 1 ≦k&lt;Fmax) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). Also, if the bit rate information indicates that the coding bit rate is BR 2 , band division section  2601  divides a part for which the band is greater than or equal to Max 2  (Max 2 ≦k&lt;Fmax) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). And if the bit rate information indicates that the coding bit rate is BR 3 , band division section  2601  divides a part for which the band is greater than or equal to Max 3  (Max 3 ≦k&lt;Fmax) within input spectrum X(k) into P subbands SB p  (p=0, 1, . . . , P−1). 
     Here, Fmax is the maximum band value, and the relationship of Max 1 , Max 2 , and Max 3  is Max 1 &lt;Max 2 &lt;Max 3 . 
     That is to say, if bit rate information indicates that the coding bit rate is BR 1 , a wide setting is made for a high-band part of an input spectrum subject to band enhancement coded information calculation by band enhancement coding section  2501 . Also, if bit rate information indicates that the coding bit rate is BR 3 , a narrow setting is made for a high-band part of an input spectrum subject to band enhancement coded information calculation by band enhancement coding section  2501 . And if bit rate information indicates that the coding bit rate is BR 2 , a setting between the above two(wide setting and narrow setting) is made for a high-band part of an input spectrum subject to band enhancement coded information calculation. 
     Then band division section  2601  outputs bandwidth BW p  (p=0, 1, . . . , P−1) and initial index BS p  (p=0, 1, . . . , P−1) of each subband to filtering section  1303 , search section  1305 , and multiplexing section  1307  as band division information. Below, a part in subband SB p  within input spectrum X(k) is denoted as subband spectrum X p (k) (BS p ≦k&lt;BS p +BW p ). 
     First layer decoded spectrum C 1 ( k ) is input to addition spectrum calculation section  2602  from orthogonal transform processing section  2405 . Also, decoded residual spectrum D 1 ( k ) is input to addition spectrum calculation section  2602  from residual spectrum coding section  2502 . Addition spectrum calculation section  2602  adds these two spectra in the frequency domain as shown in equation 31, and calculates addition spectrum A(k). Then addition spectrum calculation section  2602  outputs addition spectrum A(k) to filter state setting section  1302 .
 
[31]
 
 A ( k )= C 1( k )+ D 1( k )( k= 0, . . . F max)  (Equation 31)
 
     Thereafter, in the same way as in Embodiment 2, band enhancement coded information is generated by means of filter state setting section  1302 , filtering section  1303 , search section  1305 , pitch coefficient setting section  1304 , gain coding section  1306 , and multiplexing section  1307 , and the band enhancement coded information is output to multiplexing section  2503 . 
     In Embodiment 2, filter state setting section  1302  set first layer decoded spectrum C(k) input from orthogonal transform processing section  1005  as a filter state used by filtering section  1303 . In contrast, in this embodiment, filter state setting section  1302  sets addition spectrum A(k) input from addition spectrum calculation section  2602  as a filter state used by filtering section  1303 . Then addition spectrum A(k) is stored as a filter internal state (filter state) in an entire frequency band 0≦k&lt;Fmax spectrum S(k) low-band part ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 )) band in filtering section  1303 . 
       FIG. 27  is a block diagram showing the internal configuration of residual spectrum coding section  2502 . Residual spectrum coding section  2502  mainly comprises coding target spectrum calculation section  2701 , shape coding section  2702 , gain coding section  2703 , and multiplexing section  2704 . These sections perform the following operations. 
     Input spectrum X(k) and first layer decoded spectrum C 1 ( k ) are input to coding target spectrum calculation section  2701  from orthogonal transform processing section  2405 . Also, bit rate information is input to coding target spectrum calculation section  2701  from outside. Coding target spectrum calculation section  2701  first calculates difference spectrum B(k) between input spectrum X(k) and first layer decoded spectrum C 1 ( k ). Below, a part in subband SB p  within difference spectrum B(k) is denoted as subband spectrum B p (k) (BS p ≦k&lt;BS p +BW p ).
 
[32]
 
 B ( k )= X ( k )− C 1( k )( k= 0, . . . , F max)  (Equation 32)
 
     Then, coding target spectrum calculation section  2701  sets a partial band spectrum within difference spectrum B(k) obtained by means of equation 32 as an coding target spectrum according to the bit rate information. 
     Specifically, if the bit rate information indicates that the coding bit rate is BR 1 , coding target spectrum calculation section  2701  sets a part for which the band is less than or equal to Max 1  (0≦k&lt;Max 1 ) within difference spectrum B(k) as coding target spectrum D(k). Also, if the bit rate information indicates that the coding bit rate is BR 2 , band division section  2601  sets a part for which the band is less than or equal to Max 2  (0≦k&lt;Max 2 ) within difference spectrum B(k) as coding target spectrum D(k). And if the bit rate information indicates that the coding bit rate is BR 3 , band division section  2601  sets a part for which the band is less than or equal to Max 3  (0≦k&lt;Max 3 ) within difference spectrum B(k) as coding target spectrum D(k). 
     As stated above, the relationship of Max 1 , Max 2 , and Max 3  is Max 1 ≦Max 2 &lt;Max 3 . 
     That is to say, if bit rate information indicates that the coding bit rate is BR 1 , coding target spectrum calculation section  2701  makes a narrow bandwidth setting for spectrum (coding target spectrum) D(k) subject to coding by residual spectrum coding section  2502 . Also, if bit rate information indicates that the coding bit rate is BR 3 , coding target spectrum calculation section  2701  makes a wide coding target spectrum bandwidth setting. And if bit rate information indicates that the coding bit rate is BR 2 , coding target spectrum calculation section  2701  sets a coding target spectrum bandwidth between the above two (between wide setting and narrow setting). 
     Then coding target spectrum calculation section  2701  outputs set coding target spectrum D(k) to shape coding section  2702 . 
     Shape coding section  2702  performs quantization on a subband-by-subband basis on coding target spectrum D(k) input from coding target spectrum calculation section  2701 . Specifically, shape coding section  2702  first divides coding target spectrum D(k) into L subbands. Then, for each of the L subbands, shape coding section  2702  searches an internal shape codebook comprising SQ shape code vectors, and finds an index of a shape code vector for which evaluation measure Shape_q(i) in equation 33 below is maximal. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     33 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Shape_q 
                       ⁢ 
                       
                         ( 
                         i 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           { 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 BW 
                                 ⁡ 
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   D 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       + 
                                       
                                         BS 
                                         ⁡ 
                                         
                                           ( 
                                           j 
                                           ) 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 · 
                                 
                                   SC 
                                   k 
                                   i 
                                 
                               
                               ) 
                             
                           
                           } 
                         
                         2 
                       
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             BW 
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                           
                             SC 
                             k 
                             i 
                           
                           · 
                           
                             SC 
                             k 
                             i 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         L 
                         - 
                         1 
                       
                       , 
                       
                         i 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         SQ 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   33 
                   ] 
                 
               
             
           
         
       
     
     In this equation, SC i   k  indicates a shape code vector configuring a shape codebook, i indicates a shape code vector index, and k indicates a shape code vector element index. Also, BW(j) represents the bandwidth of a band for which the band index is j, and BS(j) represents the minimum index of a spectrum configuring a band for which the band index is j. 
     Shape coding section  2702  outputs shape code vector index S_max for which evaluation measure Shape_q(i) in equation 33 above is maximal to multiplexing section  2704  as shape coded information. Also, shape coding section  2702  calculates ideal gain Gain_i(j) in accordance with equation 34 below, and outputs this to gain coding section  2703 . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Gain_i 
                       ⁢ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                     = 
                     
                       
                         { 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               BW 
                               ⁡ 
                               
                                 ( 
                                 j 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 D 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     
                                       BS 
                                       ⁡ 
                                       
                                         ( 
                                         j 
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               
                                 SC 
                                 k 
                                 
                                   S 
                                   ⁢ 
                                   _ 
                                   ⁢ 
                                   max 
                                 
                               
                             
                             ) 
                           
                         
                         } 
                       
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             BW 
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                           
                             SC 
                             k 
                             
                               S 
                               ⁢ 
                               _ 
                               ⁢ 
                               max 
                             
                           
                           · 
                           
                             SC 
                             k 
                             
                               S 
                               ⁢ 
                               _ 
                               ⁢ 
                               max 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         L 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   34 
                   ] 
                 
               
             
           
         
       
     
     Also, shape coding section  2702  outputs a shape information decoded value obtained by performing inverse quantization (local decoding) of shape coded information to gain coding section  2703 . Here, a shape information decoded value found as a shape value is denoted as Shape_q′(k). 
     Gain coding section  2703  directly quantizes ideal gain Gain_i(j) input from shape coding section  2702  in accordance with equation 9. Here too, gain coding section  2703  treats ideal gain as an L-dimensional vector, searches an internal gain codebook comprising GQ gain code vectors, and performs vector quantization. 
     Gain coding section  2703  finds gain code vector index G_min that minimizes square error Gain_q(i) in equation 9. Gain coding section  2703  outputs G_min to multiplexing section  2704  as gain coded information. 
     Also, gain coding section  2703  applies a gain information decoded value obtained by performing inverse quantization (local decoding) on gain coded information to a shape information decoded value input from shape coding section  2702 , and calculates a residual spectrum decoded value (hereinafter referred to as decoded residual spectrum D 1 ( k )) as shown in equation 35. Here, in equation 35, Shape_q′(k) is a decoded shape value and Gain_q′(k) indicates a decoded gain. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     35 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     D 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       Gain_q 
                       ′ 
                     
                     ⁢ 
                     
                       
                         ( 
                         j 
                         ) 
                       
                       · 
                       
                         Shape_q 
                         ′ 
                       
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 k 
                                 = 
                                 
                                   BL 
                                   j 
                                 
                               
                               , 
                               … 
                               ⁢ 
                               
                                   
                               
                               , 
                               
                                 BH 
                                 j 
                               
                             
                           
                         
                         
                           
                             
                               
                                 j 
                                 = 
                                 0 
                               
                               , 
                               … 
                               ⁢ 
                               
                                   
                               
                               , 
                               
                                 L 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   35 
                   ] 
                 
               
             
           
         
       
     
     Then gain coding section  2703  outputs decoded residual spectrum D 1 ( k ) to band enhancement coding section  2501 . 
     Multiplexing section  2704  multiplexes shape coded information and gain coded information input from shape coding section  2702  and gain coding section  2703  respectively, and outputs the multiplexed information to multiplexing section  2503  as residual spectrum coded information. 
     This concludes a description of the configuration of encoding apparatus  131 . 
     A conceptual diagram of coding processing with an above-described configuration and decoding processing with a configuration described later herein is shown in  FIG. 28 .  FIG. 28  is a drawing showing conceptually a correspondence relationship between an encoded/decoded spectrum band and amount of information (coding bit rate) in a coding section/decoding section of each layer. 
     In  FIG. 28 , part “A” indicates a band of a spectrum encoded/decoded by first layer coding section  2402  and first layer decoding section  2403 . Also, part “B” indicates a band of a spectrum encoded/decoded by residual spectrum coding section  2502  and residual spectrum decoding section  2902  described later herein within a band of a spectrum encoded/decoded by second layer coding section  2406  and second layer decoding section  2805  described later herein. And part “C” indicates a band of a spectrum encoded/decoded by band enhancement coding section  2501  and band enhancement decoding section  2903  described later herein within a band of a spectrum encoded/decoded by second layer coding section  2406  and second layer decoding section  2805  described later herein. 
     If bit rate information indicates that the coding bit rate is a low bit rate (BR 1 ), band enhancement coding section  2501  and band enhancement decoding section  2903  make corresponding part “C” wide, and residual spectrum coding section  2502  and residual spectrum decoding section  2902  make corresponding part “B” narrow (see  FIG. 28(   a )). On the other hand, if bit rate information indicates that the coding bit rate is a high bit rate (BR 3 ), band enhancement coding section  2501  and band enhancement decoding section  2903  make corresponding part “C” narrow, and residual spectrum coding section  2502  and residual spectrum decoding section  2902  make corresponding part “B” wide (see  FIG. 28(   c )). And if bit rate information indicates that the coding bit rate is BR 2 , band enhancement coding section  2501  and band enhancement decoding section  2903  make a corresponding part “C” setting approximately midway between that when the coding bit rate is BR 1  and that when the coding bit rate is BR 3  (see  FIG. 28(   b )). 
     Thus, in this embodiment, a band of a spectrum that is encoded/decoded by a coding section/decoding section is set adaptively according to a coding bit rate indicated by bit rate information. By this means, an input signal can be encoded/decoded efficiently even if the coding bit rate changes. 
     Decoding apparatus  133  according to this embodiment will now be described. 
       FIG. 29  is a block diagram showing the internal principal-part configuration of decoding apparatus  133 . Decoding apparatus  133  mainly comprises coded information demultiplexing section  2801 , first layer decoding section  2802 , up-sampling processing section  2803 , orthogonal transform processing section  2804 , second layer decoding section  2805 , and orthogonal transform processing section  2806 . These sections perform the following operations. 
     Coded information transmitted from encoding apparatus  131  via channel  102  is input to coded information demultiplexing section  2801 . Coded information demultiplexing section  2801  demultiplexes the input coded information into first layer coded information, second layer coded information, and bit rate information, outputs the first layer coded information to first layer decoding section  2802 , and outputs the second layer coded information and bit rate information to second layer decoding section  2805 . 
     First layer decoding section  2802  decodes the first layer coded information input from coded information demultiplexing section  2801  and generates a first layer decoded signal, and outputs the generated first layer decoded signal to up-sampling processing section  2803 . The operation of first layer decoding section  2802  is similar to that of first layer decoding section  2403  shown in  FIG. 24 , and therefore a detailed description thereof is omitted here. 
     Up-sampling processing section  2803  performs up-sampling of the sampling frequency of a first layer decoded signal input from first layer decoding section  2802  from SR base  to SR input , and outputs an obtained post-up-sampling first layer decoded signal to orthogonal transform processing section  2804 . 
     Orthogonal transform processing section  2804  performs orthogonal transform processing (MDCT) on a post-up-sampling first layer decoded signal input from up-sampling processing section  2803 . Then orthogonal transform processing section  2804  outputs obtained post-up-sampling first layer decoded signal MDCT coefficient (hereinafter referred to as first layer decoded spectrum) C 1 ( k ) to second layer decoding section  2805 . The operation of orthogonal transform processing section  2804  is similar to the processing on a post-up-sampling first layer decoded signal by orthogonal transform processing section  2405  shown in  FIG. 24 , and therefore a detailed description thereof is omitted here. 
     Second layer decoding section  2805  generates output spectrum C 2 ( k ) using a high-band component using first layer decoded spectrum C 1 ( k ) input from orthogonal transform processing section  2804  and second layer coded information and bit rate information input from coded information demultiplexing section  2801 . Then second layer decoding section  2805  outputs generated output spectrum C 2 ( k ) to orthogonal transform processing section  2806 . Details of the processing performed by second layer decoding section  2805  will be given later herein. 
     Orthogonal transform processing section  2806  executes an orthogonal transform on output spectrum C 2 ( k ) input from second layer decoding section  2805 , and converts it to a time-domain signal. Orthogonal transform processing section  2806  outputs the obtained signal as an output signal. The operation of orthogonal transform processing section  2806  is similar to the processing by orthogonal transform processing section  802  shown in  FIG. 8 , and therefore a detailed description thereof is omitted here. 
       FIG. 30  is a block diagram showing the internal configuration of second layer decoding section  2805  shown in  FIG. 29 . Second layer decoding section  2805  mainly comprises demultiplexing section  2901 , residual spectrum decoding section  2902 , and band enhancement decoding section  2903 . 
     Second layer coded information is input to demultiplexing section  2901  from coded information demultiplexing section  2801 . Demultiplexing section  2901  demultiplexes the second layer coded information into residual spectrum coded information and band enhancement coded information. Demultiplexing section  2901  outputs the residual spectrum coded information to residual spectrum decoding section  2902 , and outputs the band enhancement coded information to band enhancement decoding section  2903 . If demultiplexing into residual spectrum coded information and band enhancement coded information has been performed in coded information demultiplexing section  2801 , demultiplexing section  2901  need not be provided. 
     Residual spectrum decoding section  2902  decodes residual spectrum coded information input from demultiplexing section  2901 , and calculates decoded residual spectrum D 1 ( k ). Then residual spectrum decoding section  2902  outputs obtained decoded residual spectrum D 1 ( k ) to band enhancement decoding section  2903 . Details of the processing performed by residual spectrum decoding section  2902  will be given later herein. 
     Band enhancement coded information is input to band enhancement decoding section  2903  from demultiplexing section  2901 . Also, first layer decoded spectrum C 1 ( k ) is input to band enhancement decoding section  2903  from orthogonal transform processing section  2804 . Furthermore, bit rate information is input to band enhancement decoding section  2903  from coded information demultiplexing section  2801 . In addition, decoded residual spectrum D 1 ( k ) is input to band enhancement decoding section  2903  from residual spectrum decoding section  2902 . Band enhancement decoding section  2903  calculates output spectrum C 2 ( k ) from these items of information, and outputs this to orthogonal transform processing section  2806 . Details of the processing performed by band enhancement decoding section  2903  will be given later herein. 
       FIG. 31  is a block diagram showing the internal configuration of residual spectrum decoding section  2902 . Residual spectrum decoding section  2902  mainly comprises demultiplexing section  3001 , shape decoding section  3002 , and gain decoding section  3003 . 
     Residual spectrum coded information is input to demultiplexing section  3001  from demultiplexing section  2901 . Demultiplexing section  3001  demultiplexer the residual spectrum coded information into shape coded information and gain coded information, outputs the shape coded information to shape decoding section  3002 , and outputs the gain coded information to gain decoding section  3003 . 
     Shape coded information is input to shape decoding section  3002  from demultiplexing section  3001 . Also, bit rate information is input to shape decoding section  3002  from coded information demultiplexing section  2801 . Shape decoding section  3002  incorporates a shape codebook of the same kind as the shape codebook with which shape coding section  2702  is provided, and searches the shape codebook with shape coded information S_max input from demultiplexing section  3001  as an index. Shape decoding section  3002  outputs a found shape code vector to gain decoding section  3003  as a shape value of a band spectrum corresponding to bit rate information input from coded information demultiplexing section  2801 . Here, a shape code vector found as a shape value is denoted as Shape_q′(k). 
     Here, shape decoding section  3002  calculates a band corresponding to bit rate information by means of the same kind of method as described for coding target spectrum calculation section  2701 . 
     Gain decoding section  3003  incorporates a gain codebook of the same kind as the gain codebook with which gain coding section  2703  is provided, and uses this gain codebook to perform inverse quantization of a gain value from gain coded information in accordance with equation 16. Here too, a gain value is treated as an L-dimensional vector, and vector inverse quantization is performed. That is to say, gain code vector GC j   G     —     min  corresponding to gain coded information G_min is taken directly as gain value Gain_q′(j). 
     Then, using a gain value obtained by inverse quantization and a shape value input from shape decoding section  3002 , gain decoding section  3003  calculates decoded residual spectrum D 1 ( k ) for a band corresponding to bit rate information input from coded information demultiplexing section  2801  in accordance with equation 35, and outputs calculated decoded residual spectrum D 1 ( k ) to band enhancement decoding section  2903 . In spectrum (MDCT coefficient) inverse quantization, if k is present in B(j″) through B(j″+1)−1, gain value Gain_q′(j) has the value of Gain_q′(j″). 
     As with shape decoding section  3002 , gain decoding section  3003  calculates a band corresponding to bit rate information by means of the same kind of method as described for coding target spectrum calculation section  2701 . 
       FIG. 32  is a block diagram showing the internal configuration of band enhancement decoding section  2903  shown in  FIG. 30 . Band enhancement decoding section  2903  mainly comprises demultiplexing section  3101 , filter state setting section  3102 , filtering section  3103 , gain decoding section  3104 , spectrum adjustment section  3105 , and addition spectrum calculation section  3106 . 
     Demultiplexing section  3101  demultiplexes band enhancement coded information input from demultiplexing section  2901  into optimum pitch coefficient T′, which is filtering related information, and a post-coding variation V q (j) index, which is gain related information. Then demultiplexing section  3101  outputs optimum pitch coefficient T′ to filtering section  3103 , and outputs the post-coding variation V q (j) index to gain decoding section  3104 . If demultiplexing into optimum pitch coefficient T′ and a post-coding variation V q (j) index has been performed in coded information demultiplexing section  2801  or demultiplexing section  2901 , demultiplexing section  3101  need not be provided. 
     First layer decoded spectrum C 1 ( k ) is input to addition spectrum calculation section  3106  from orthogonal transform processing section  2804 . Also, decoded residual spectrum D 1 ( k ) is input to addition spectrum calculation section  3106  from residual spectrum decoding section  2902 . Addition spectrum calculation section  3106  adds these two spectra in the frequency domain as shown in equation 31, and calculates addition spectrum A(k). Then addition spectrum calculation section  3106  outputs addition spectrum A(k) to filter state setting section  3102 . 
     Filter state setting section  3102  sets addition spectrum A(k) input from addition spectrum calculation section  3106  as a filter state used by filtering section  3103 . Here, if an entire frequency band 0≦k&lt;Fmax spectrum in filtering section  3103  is called Z(k) for convenience, of spectrum Z(k), addition spectrum A(k) is stored in a band corresponding to bit rate information as a filter internal state (filter state). The configuration and operation of filter state setting section  3102  are similar to those of filter state setting section  502  shown in  FIG. 5 , and therefore a detailed description thereof is omitted here. 
     Filtering section  3103  is provided with a multi-tap pitch filter (that is, the number of taps is greater than 1). Filtering section  3103  filters addition spectrum A(k) for a band corresponding to bit rate information input from coded information demultiplexing section  2801  based on a filter state set by filter state setting section  3102 , pitch coefficient T′ input from demultiplexing section  3101 , and a filter coefficient stored internally beforehand. Then filtering section  3103  calculates estimated spectrum X′(k) of input spectrum X(k) as shown in equation 36. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     36 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       X 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           - 
                           1 
                         
                       
                       1 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         β 
                         i 
                       
                       · 
                       
                         
                           Z 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               T 
                               + 
                               i 
                             
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   36 
                   ] 
                 
               
             
           
         
       
     
     Here, filter state setting section  3102  and filtering section  3103  use a high-band part of a spectrum calculated by means of the same kind of method as described for band division section  2601  as a band corresponding to bit rate information. 
     The transfer function shown in equation 13 is also used by filtering section  3103 . Filtering section  3103  outputs estimated spectrum X′(k) obtained by filtering to spectrum adjustment section  3105 . 
     Gain decoding section  3104  decodes a post-coding variation V q (j) index input from demultiplexing section  3101  for a band corresponding to bit rate information input from coded information demultiplexing section  2801 , and finds post-coding variation V q (j), which is a variation V(j) quantization value. Here, the gain codebook used for decoding an index of post-coding variation V q (j) is incorporated in gain decoding section  3104 , and is similar to the gain codebook used by gain coding section  506  shown in  FIG. 5 . Gain decoding section  3104  outputs post-coding variation V q (j) obtained by decoding to spectrum adjustment section  3105 . 
     Here, gain decoding section  3104  uses a high-band part of a spectrum calculated by means of the same kind of method as described for band division section  2601  as a band corresponding to bit rate information. 
     Spectrum adjustment section  3105  multiplies estimated spectrum X′(k) input from filtering section  3103  by post-coding variation V q (j) of each subband input from gain decoding section  3104  for a high-band part specified by bit rate information input from coded information demultiplexing section  2801  in accordance with equation 37. 
     Here, spectrum adjustment section  3105  uses a high-band part of a spectrum calculated by means of the same kind of method as described for band division section  2601  as a band corresponding to bit rate information. By this means, spectrum adjustment section  3105  adjusts the spectrum shape in an estimated spectrum high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax) or (Max 3 ≦k&lt;Fmax)), generates output spectrum C 2 ( k ), and outputs this to orthogonal transform processing section  2806 . 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       37 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           X 
                           ′ 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       · 
                       
                         
                           V 
                           q 
                         
                         ⁡ 
                         
                           ( 
                           j 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   37 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     
                       
                         
                           
                             Max 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           ≤ 
                           k 
                           &lt; 
                           
                             F 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             max 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   or 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   Max 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 ≤ 
                                 k 
                                 &lt; 
                                 
                                   F 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   max 
                                 
                               
                             
                             
                               
                                 
                                   or 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   Max 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   3 
                                 
                                 ≤ 
                                 k 
                                 &lt; 
                                 
                                   F 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   max 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             j 
                             = 
                             0 
                           
                           , 
                           … 
                           ⁢ 
                           
                               
                           
                           , 
                           
                             J 
                             - 
                             1 
                           
                         
                       
                       
                         
                             
                         
                       
                     
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     In equation 37, j indicates a subband index when gain is encoded, and is set according to spectrum index k. That is to say, for spectrum index k included in a subband for which the subband index is j″, estimated spectrum X′(k) is multiplied by V q (j″). 
     Here, a low-band part ((0≦k&lt;Max 1 ) or (0≦k&lt;Max 2 ) or (Max 3 ≦k&lt;Fmax)) of output spectrum C 2 ( k ) comprises addition spectrum A(k) obtained by adding first layer decoded spectrum C 1 ( k ) and decoded residual spectrum D 1 ( k ), and a high-band part ((Max 1 ≦k&lt;Fmax) or (Max 2 ≦k&lt;Fmax) or (Max 3 ≦k&lt;Fmax)) of output spectrum C 2 ( k ) comprises post-spectrum-shape-adjustment estimated spectrum X′(k). 
     This concludes a description of the internal configuration of decoding apparatus  113 . 
     Thus, according to this embodiment, an encoding apparatus/decoding apparatus employs a configuration whereby band setting according to a band enhancement method is switched adaptively according to conditions at the time of coding (for example, the coding bit rate). By this means, coding efficiency can be improved in line with conditions at the time of coding. 
     Specifically, for example, if the bit rate at the time of coding is a low bit rate, band division section  2601  makes a wide setting for a band generated by means of a band enhancement technology that is more effective with a low bit rate, and makes a narrow setting for a band quantized by means of a spectrum coding technology other than a band enhancement technology. Also, if the bit rate at the time of coding is a high bit rate, band division section  2601  makes a narrow setting for a band generated by means of a band enhancement technology, and makes a wide setting for a band quantized by means of a spectrum coding technology (a technology other than a band enhancement technology) that encodes a spectrum shape more precisely. 
     When performing band enhancement coding/decoding, an encoding apparatus/decoding apparatus can improve the coding efficiency of band enhancement coding by using a high-precision spectrum that can be obtained at the time of coding/decoding (an addition spectrum resulting from addition of a first layer decoded spectrum and decoded residual spectrum) as a low-band part decoded spectrum. In this way, the quality of a decoded signal can be greatly improved by means of the method described in this embodiment. 
     In this embodiment, a configuration has been described whereby a narrow setting is made for a band of a spectrum that is encoded/decoded by band enhancement coding section  2501  and band enhancement decoding section  2903  when bit rate information indicates that the coding bit rate is the highest bit rate, but the present invention is not limited to this. For example, the present invention can be applied in a similar way to a configuration whereby a band of a spectrum encoded/decoded by band enhancement coding section  2501  and band enhancement decoding section  2903  is eliminated. In this case, band enhancement coding section  2501  and band enhancement decoding section  2903  are unnecessary in second layer coding section  2406  and second layer decoding section  2805  respectively, and a spectrum of all bands becomes subject to quantization in residual spectrum coding section  2502  and residual spectrum decoding section  2902 . Also, at this time, the entire amount of information (bits) that can be used by second layer coding section  2406  and second layer decoding section  2805  is assigned to residual spectrum coding section  2502  and residual spectrum decoding section  2902 . A configuration such as described above in which a band encoded/decoded by a band enhancement coding section and band enhancement decoding section is eliminated has been confirmed by experimentation to be particularly effective when the coding bit rate is extremely high. 
     In this embodiment, a case such as shown in  FIG. 28  in which band “C” subject to coding by band enhancement coding section  2501  and band “B” subject to coding by residual spectrum coding section  2502  do not overlap in the frequency domain has been described as an example. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration other than that shown in  FIG. 28 . For example, a conceptual diagram of another configuration is shown in  FIG. 33 .  FIG. 33  is a drawing showing conceptually another correspondence relationship between an encoded/decoded spectrum band and amount of information (coding bit rate) in a coding section/decoding section of each layer. 
     In the case of a configuration such as shown in  FIG. 33 , processing that is partially different from the kind of coding processing described in this embodiment is performed. Specifically, in second layer coding section  2406 , coding is first performed by residual spectrum coding section  2502 , and then coding is performed by band enhancement coding section  2501  using a decoded residual spectrum. However, in the case of the configuration shown in  FIG. 33 , coding is first performed by band enhancement coding section  2501 , and an obtained residual spectrum of a high-band spectrum and input spectrum is encoded by residual spectrum coding section  2502 . 
     In this embodiment, a configuration whereby a low-band part is encoded/decoded by first layer coding section  2402  and first layer decoding section  2403  has been described as an example, but the present invention is not limited to this, and can also be applied in a similar way to a configuration in which first layer coding section  2402  and first layer decoding section  2403  are not present. At this time, a configuration is used in which residual spectrum coding section  2502  and residual spectrum decoding section  2902  encode/decode a band set for an input spectrum itself based on bit rate information. 
     In this embodiment, no particular explanation has been given of what kind of bit assignment is performed for band enhancement coding section  2501  and residual spectrum coding section  2502  according to bit rate information at the time of coding. An example of a possible bit assignment method is the use of a configuration whereby bits assigned to band enhancement coding section  2501  are always fixed, and bits assigned to residual spectrum coding section  2502  are variable. However, the present invention is not limited to a bit assignment method for band enhancement coding section  2501  and residual spectrum coding section  2502 , and can also be applied in a similar way to a configuration that employs a bit assignment method other than the above. An example of a method other than the above is the use of a configuration whereby, as a coding bit rate indicated by bit rate information increases for band enhancement coding section  2501  and residual spectrum coding section  2502 , the number of bits assigned to them both is increased. Another option is a configuration whereby, as a coding bit rate indicated by bit rate information increases, the number of bits assigned to band enhancement coding section  2501  is reduced, and the number of bits assigned to residual spectrum coding section  2502  is increased. 
     In the above description, a case in which a coding bit rate is used as an example of conditions at the time of coding has been taken as an example, and a case in which band setting is performed according to the coding bit rate has been described, but provision may also be made for the input signal sampling frequency or a coding parameter such as a quantization gain to be used instead of the coding bit rate. If band setting is performed according to the input signal sampling frequency, a possible configuration example is one whereby processing when the coding bit rate is a low bit rate in this embodiment is used if the sampling frequency is greater than or equal to a predetermined threshold value, and processing when the coding bit rate is a high bit rate in this embodiment is used if the sampling frequency is less than the threshold value. Also, with regard to a coding parameter such as quantization gain, a possible configuration example is one whereby processing when the coding bit rate is a low bit rate in this embodiment is used if, for example, gain sampled by the first layer coding section (adaptive excitation gain, fixed excitation gain, or the like) is greater than or equal to a predetermined threshold value, and processing when the coding bit rate is a high bit rate in this embodiment is used if this gain is less than the threshold value. 
     This concludes a description of embodiments of the present invention. 
     In the above embodiments, a band setting section decides band setting information according to an energy ratio of a low-band part and high-band part of an input spectrum or a difference spectrum between an input spectrum and first layer decoded spectrum. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration in which band setting information is decided using other information. One example of such a configuration is one whereby tonality analysis is performed on an input spectrum or a difference spectrum between an input spectrum and first layer decoded spectrum, and the band setting section decides band setting information by the degree of tonality. In this case, it is necessary for a configuration element that calculates tonality to be newly provided. A tonality calculation method (detection method) used in this case is disclosed in detail in Patent Literature 2 and so forth. 
     Specifically, if input signal tonality is low—that is, if an input signal has a marked tendency toward being speech—the band setting section makes a narrower setting for a low-band part and a wider setting for a high-band part. This corresponds to a case in which the value of band setting information Band_Setting is 0 in these embodiments. By this means, low-band part spectral data that greatly influences the quality of a decoded signal when an input signal is speech can be encoded intensively by means of a shape-gain coding method, and the quality of a decoded signal can be increased. 
     Also, if input signal tonality is high—that is, if an input signal has a marked tendency toward being audio (music)—the band setting section makes a wider setting for a low-band part and a narrower setting for a high-band part. This corresponds to a case in which the value of band setting information Band_Setting is 1 in these embodiments. By this means, coding distortion can be reduced with a shape-gain coding method up to a higher band part, and bandwidth limitation that greatly influences the quality of a decoded signal when an input signal is audio can be improved. 
     Also, when tonality is used to decide band setting information, if tonality is calculated by a configuration element other than the band setting section, the amount of computation necessary for tonality calculation can be reduced by using a configuration whereby calculated tonality is input to the band setting section. In this case, it is sufficient to input tonality to the band setting section, and it is not necessary to input an input spectrum or difference spectrum. 
     In the above embodiments, a case in which the value of band setting information is one of two values, 0 or 1, has been given as an example, but the present invention is not limited to this, and can also be applied in a similar way to a configuration in which band setting information can have two or more values. Although the number of bits (amount of information) necessary for band setting information increases, increasing the possible values of band setting information and increasing the number of band setting patterns enables band setting to be performed that is more appropriate for an input signal. For example, by providing for four possible band setting values—0, 1, 2, and 3—and setting one of these four values according to the energy ratio of a low-band part and high-band part, a band quantized by a coding section of each layer can be set more finely according to the input signal. 
     In the above embodiments, a configuration in which a band setting section performs band adjustment for each processed frame has been described as an example. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby band adjustment is performed in units of processing of several frames, for example. By means of a configuration of this kind, the amount of processing computation by the band setting section can be reduced, and input signal discontinuity that may occur due to band adjustment for each processed frame can be alleviated. 
     In the above embodiments, a configuration in which a band setting section performs band adjustment independently for each processed frame has been described as an example. However, the present invention is not limited to this, and can also be applied in a similar way to a configuration whereby a band of a current frame is adjusted (set) based on band setting information for a past processed frame. One possible configuration example is one whereby band setting information for several frames back is used to smooth parameters (first band energy, second band energy, and so forth) at the time of current frame band setting on a time axis, and decide current frame band setting information. Another possible configuration example is one whereby band setting information itself is smoothed after delaying band setting information for several frames so that band setting information itself does not fluctuate rapidly. By means of a configuration of this kind, rapid fluctuation of band setting information for each processed frame can be prevented, and decoded signal discontinuity that may occur due to band adjustment for each processed frame can be alleviated. 
     In above Embodiment 1 through Embodiment 3, an encoding apparatus has been described as adaptively deciding an extension band setting according to an input signal characteristic, and in above Embodiment 4, an encoding apparatus has been described as adaptively deciding an extension band setting according to a coding parameter indicating conditions at the time of coding. However, it is also possible for an encoding apparatus to input both an input signal and a coding parameter, and decide an extension band setting based on both an input signal characteristic and a coding parameter. For example, one possible actual method is first to set an extension band to some extent by means of a coding parameter (such as a coding bit rate), and then to perform finer extension band setting adjustment using an input signal characteristic (such as a high-band/low-band energy ratio). By this means, more appropriate band setting can be performed, enabling more efficient encoding to be performed, and also enabling the quality of a decoded signal in a decoding apparatus to be improved. Alternatively, it is also possible for an encoding apparatus to input both an input signal and a coding parameter, to select either the input signal characteristic or the coding parameter by determining which of these parameters is suitable for use, and to decide an extension band setting based on the selected parameter. 
     An encoding apparatus and decoding apparatus according to the present invention are not limited to the above embodiments, and it is possible for such apparatus to be implemented with various modifications. For example, the embodiments may be combined to be implemented as appropriate. 
     A decoding apparatus according to each of the above embodiments has been assumed to perform processing using coded information transmitted from an encoding apparatus according to each of the above embodiments. However, the present invention is not limited to this, and as long as coded information includes a necessary parameter and data, it is possible for processing to be performed with coded information that is not necessarily from an encoding apparatus according to an above embodiment. 
     The present invention can also be applied to, and the same kind of operation and effects as in these embodiments can also be obtained in, a case in which recording and writing of a signal processing program is performed in/on/to a machine-readable recording medium such as memory or a disk, tape, CD, or DVD, and operation thereof is performed. 
     In the above embodiments, a case has been described by way of example in which the present invention is configured as hardware, but it is also possible for the present invention to be implemented by software. 
     The function blocks used in the above embodiments are implemented as LSIs typically comprising integrated circuitry. These may be implemented individually as single chips, or a single chip may incorporate some or all of them. Here, the term LSI has been used, but the terms IC, system LSI, super LSI, and ultra LSI may also be used according to differences in the degree of integration. 
     Implementation of integrated circuitry is not limited to an LSI method, and implementation by means of dedicated circuitry or a general-purpose processor may also be used. An FPGA (Field Programmable Gate Array) for which programming is possible after LSI fabrication, or a reconfigurable processor allowing reconfiguration of circuit cell connections and settings within an LSI, may also be used. 
     Furthermore, in the event of the introduction of an integrated circuit implementation technology whereby LSI technology is replaced by a different technology as an advance in, or derivation from, semiconductor technology, integration of the function blocks may of course be performed using that technology. The application of biotechnology or the like is also a possibility. 
     The disclosures of Japanese Patent Application No. 2009-244838, filed on Oct. 23, 2009, and Japanese Patent Application No. 2009-272194, filed on Nov. 30, 2009, including the specifications, drawings and abstracts, are incorporated herein by reference in their entirety. 
     INDUSTRIAL APPLICABILITY 
     An encoding apparatus, decoding apparatus, and methods thereof according to the present invention enable the quality of a decoded signal to be improved when performing band enhancement using a low-band part spectrum and estimating a high-band part spectrum, and are suitable for use in a packet communication system, mobile communication system, or the like, for example. 
     REFERENCE SIGNS LIST 
     
         
           101 ,  111 ,  121 ,  131  Encoding apparatus 
           102  Channel 
           103 ,  113 ,  123 ,  133  Decoding apparatus 
           201 ,  802 ,  1005 ,  1404 ,  1406 ,  2405 ,  2804 ,  2806  Orthogonal transform processing section 
           202  Coding section 
           301 ,  1101 ,  1801  Band setting section 
           302 ,  1102  Low-band coding section 
           303 ,  1103 ,  1802  High-band coding section 
           902 ,  1502  Low-band decoding section 
           903 ,  1503 ,  2002  High-band decoding section 
           304 ,  404 ,  507 ,  1104 ,  1204 ,  1307 ,  1803 ,  2503 ,  2704  Multiplexing section 
           401 ,  2701  Coding target spectrum calculation section 
           402 ,  1202 ,  2702  Shape coding section 
           403 ,  506 ,  1203 ,  1306 ,  2703  Gain coding section 
           501 ,  1301 ,  1311 ,  2601  Band division section 
           502 ,  922 ,  1302 ,  1602 ,  3102  Filter state setting section 
           503 ,  923 ,  1303 ,  1603 ,  3103  Filtering section 
           505 ,  1305  Search section 
           504 ,  1304  Pitch coefficient setting section 
           801  Decoding section 
           901 ,  911 ,  921 ,  1501 ,  1601 ,  2001 ,  2901 ,  3001 ,  3101  Demultiplexing section 
           1504  Spectrum synthesis section 
           912 ,  3002  Shape decoding section 
           913 ,  924 ,  1604 ,  3003 ,  3104  Gain decoding section 
           925 ,  1605 ,  3105  Spectrum adjustment section 
           1001 ,  2401  Down-sampling processing section 
           1002 ,  2403  First layer coding section 
           1003 ,  1402 ,  2403 ,  2802  First layer decoding section 
           1004 ,  1403 ,  2404 ,  2803  Up-sampling processing section 
           1006 ,  1701 ,  2406  Second layer coding section 
           1007 ,  2407  Coded information integration section 
           1201  Difference spectrum calculation section 
           1401 ,  2801  Coded information demultiplexing section 
           1405 ,  1901 ,  2805  Second layer decoding section 
           2501  Band enhancement coding section 
           2502  Residual spectrum coding section 
           2602 ,  3106  Addition spectrum calculation section 
           2902  Residual spectrum decoding section 
           2903  Band enhancement decoding section