Abstract:
Disclosed is a spectral smoothing device with a structure whereby smoothing is performed after a nonlinear conversion has been performed for a spectrum calculated from an audio signal, and with which the amount of processing calculation is significantly reduced while maintaining excellent audio quality. With this spectral smoothing device, a sub band division unit ( 102 ) divides an input spectrum into multiple sub bands; a representative value calculation unit ( 103 ) calculates a representative value for each sub band using an arithmetic mean and a geometric mean; with respect to each representative value, a nonlinear conversion unit ( 104 ) performs a nonlinear conversion the characteristic of which is further emphasized as the value increases; and a smoothing unit ( 105 ) that smoothes the representative value which has undergone the nonlinear conversion for each sub band, at the frequency domain.

Description:
TECHNICAL FIELD 
     The present invention relates to a spectrum smoothing apparatus, a coding apparatus, a decoding apparatus, a communication terminal apparatus, a base station apparatus and a spectrum smoothing method smoothing spectrum of speech signals. 
     BACKGROUND ART 
     When speech/audio signals are transmitted in a packet communication system typified by Internet communication and a mobile communication system, a compression/coding technique is often used to improve the transmission rate of speech/audio signals. Furthermore, in recent years, in addition to a demand for simply encoding speech/audio signals at low bit rates, there is an increasing demand for a technique to encode speech/audio signals in high quality. 
     To meet this demand, studies are underway to develop various techniques to perform orthogonal transformation (i.e. time-frequency transformation) of a speech signal to extract frequency components (i.e. spectrum) of the speech signal and apply various processing such as linear transformation and non-linear transformation to the calculated spectrum to improve the quality of the decoded signal (see, for example, patent literature 1). According to the method disclosed in patent literature 1, first, a frequency spectrum contained in a speech signal of a certain time length is analyzed, and then non-linear transformation processing to emphasize greater spectrum power values is applied to the analyzed spectrum. Next, linear smoothing processing for the spectrum subjected to non-linear transformation processing, is performed in the frequency domain. After this, inverse non-linear transformation processing is performed to cancel non-linear transformation characteristics, and, furthermore, inverse smoothing processing is performed to cancel smoothing characteristics, so that noise components included in the speech signal over the entire band are suppressed. Thus, with the method disclosed in patent literature 1, all samples of a spectrum acquired from a speech signal are subjected to non-linear transformation processing and then the spectrum is smoothed, so that the speech signal is acquired in good quality. Patent literature 1 introduces transformation methods such as power transform and logarithmic transform as examples of non-linear processing. 
     CITATION LIST 
     Patent Literature 
     PTL 1 
     
         
         Japanese Patent Application Laid-Open No. 2002-244695
 
PTL 2
 
         WO 2007/037361 
       
    
     Non-Patent Literature 
     NPL 1 
     
         
         Yuichiro TAKAMIZAWA, Toshiyuki NOMURA and Masao IKEKAWA, “High-Quality and Processor-Efficient Implementation of and MPEG-2 AAC Encoder”, IEICE TRANS. INF. &amp; SYST., VOL. E86-D, No. 3 MARCH 2003 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, with the method disclosed in patent literature 1, non-linear transformation processing needs to be performed for all samples of a spectrum acquired from a speech signal, and therefore there is a problem that the amount of calculation processing is enormous. Furthermore, if only part of samples of a spectrum are extracted to reduce the amount of calculation processing, sufficiently high speech quality cannot be always achieved by simply performing spectrum smoothing after non-linear transformation. 
     Based upon a configuration for performing non-linear transformation of a spectrum value calculated from a speech signal and then smoothing the spectrum, it is an object of the present invention to provide a spectrum smoothing apparatus, a coding apparatus, a decoding apparatus, a communication terminal apparatus, a base station apparatus and a spectrum smoothing method, whereby good speech quality is maintained and the amount of calculation processing can be reduced substantially. 
     Solution to Problem 
     The spectrum smoothing apparatus according to the present invention employs a configuration to include: a time-frequency transformation section that performs a time-frequency transformation of an input signal and generates a frequency component; a subband dividing section that divides the frequency component into a plurality of subbands; a representative value calculating section that calculates a representative value of each divided subband by calculating an arithmetic mean and by using a multiplication calculation using a calculation result of the arithmetic mean; a non-linear transformation section that performs a non-linear transformation of representative values of the subbands; and a smoothing section that smoothes the representative values subjected to the non-linear transformation in the frequency domain. 
     The spectrum smoothing method according to the present invention includes: a time-frequency transformation step of performing a time-frequency transformation of an input signal and generates a frequency component; a subband division step of dividing the frequency component into a plurality of subbands; a representative value calculation step of calculating a representative value of each divided subband by calculating an arithmetic mean and by using a multiplication calculation using a calculation result of the arithmetic mean; a non-linear transformation step of performing a non-linear transformation of representative values of the subbands; and a smoothing step of smoothing the representative values subjected to the non-linear transformation in the frequency domain. 
     Advantageous Effects of Invention 
     With the present invention, it is possible to maintain good speech quality and reduce the amount of calculation processing substantially. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  provides spectrum overviews showing an overview of processing according to embodiment 1 of the present invention; 
         FIG. 2  is a block diagram showing a principal-part configuration of a spectrum smoothing apparatus according to embodiment 1; 
         FIG. 3  is a block diagram showing a principal-part configuration of a representative value calculating section according to embodiment 1; 
         FIG. 4  is an overview showing a configuration of subbands and subgroups of an input signal according to embodiment 1; 
         FIG. 5  is a block diagram showing a configuration of a communication system having a coding apparatus and decoding apparatus according to embodiment 2 of the present invention; 
         FIG. 6  is a block diagram showing an inner principal-part of the coding apparatus according to embodiment 2 shown in  FIG. 5 ; 
         FIG. 7  is a block diagram showing an inner principal-part configuration of the second layer coding section according to embodiment 2 shown in  FIG. 6 ; 
         FIG. 8  is a block diagram showing a principal-part configuration of the spectrum smoothing apparatus according to embodiment 2 shown in  FIG. 7 ; 
         FIG. 9  shows a diagram for explaining the details of the filtering processing in the filtering section according to embodiment 2 shown in  FIG. 7 ; 
         FIG. 10  is a flowchart for explaining the steps of processing for searching for optimal pitch coefficient T p ′ with respect to subband SB p  in the search section according to embodiment 2 shown in  FIG. 7 ; 
         FIG. 11  is a block diagram showing an inner principal-part configuration of the decoding apparatus according to embodiment 2 shown in  FIG. 5 ; and 
         FIG. 12  is a block diagram showing an inner principal-part configuration of the second layer decoding section according to embodiment 2 shown in  FIG. 11 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described in detail with reference to the accompanying drawings. 
     Embodiment 1 
     First, an overview of the spectrum smoothing method according to an embodiment of the present invention will be described using  FIG. 1 .  FIG. 1  shows spectrum diagrams for explaining an overview of the spectrum smoothing method according to the present embodiment. 
       FIG. 1A  shows a spectrum of an input signal. With the present embodiment, first, an input signal spectrum is divided into a plurality of subbands.  FIG. 1B  shows how an input signal spectrum is divided into a plurality of subbands. The spectrum diagram of  FIG. 1  is for explaining an overview of the present invention, and the present invention is by no means limited to the number of subbands shown in the drawing. 
     Next, a representative value of each subband is calculated. To be more specific, samples in a subband are further divided into a plurality of subgroups. Then, an arithmetic mean of absolute spectrum values is calculated per subgroup. 
     Next, a geometric mean of the arithmetic mean values of individual subgroups is calculated per subband. This geometric mean value is not an accurate geometric mean value yet, and, at this point, a value that is obtained by simply multiplying individual groups&#39; arithmetic mean values may be calculated, and an accurate geometric mean value may be found after non-linear transformation (described later). The above processing is to reduce the amount of calculation processing, and it is equally possible to find an accurate geometric mean value at this point. 
     A geometric mean value found this way may be used as a representative value of each subband.  FIG. 1C  shows representative values of individual subbands over an input signal spectrum shown with dotted lines. For ease of explanation,  FIG. 1C  shows accurate geometric mean values as representative values, instead of values obtained by simply multiplying arithmetic mean values of individual subgroups. 
     Next, referring to each subband&#39;s representative value, non-linear transformation (for example, logarithmic transform) is performed for a spectrum of an input signal such that greater spectrum power values are emphasized, and then smoothing processing is performed in the frequency domain. Afterward, inverse non-linear transformation (for example, inverse logarithmic transform) is performed, and a smoothed spectrum is calculated in each subband.  FIG. 1D  shows a smoothed spectrum of each subband over an input signal spectrum shown with dotted lines. 
     By means of this processing, it is possible to perform spectrum smoothing in the logarithmic domain while reducing speech quality degradation and reducing the amount of calculation processing substantially. Now, a configuration of a spectrum smoothing apparatus providing the above advantage, according to an embodiment of the present invention, will be described. 
     The spectrum smoothing apparatus according to the present embodiment smoothes an input spectrum, and outputs the spectrum after the smoothing (hereinafter “smoothed spectrum”) as an output signal. To be more specific, the spectrum smoothing apparatus divides an input signal every N samples (where N is a natural number), and performs smoothing processing per frame using N samples as one frame. Here, an input signal that is subject to smoothing processing is represented as “x n ” (n=0, . . . , N−1). 
       FIG. 2  shows a principal-part configuration of spectrum smoothing apparatus  100  according to the present embodiment. 
     Spectrum smoothing apparatus  100  shown in  FIG. 2  is primarily formed with time-frequency transformation processing section  101 , subband dividing section  102 , representative value calculating section  103 , non-linear transformation section  104 , smoothing section  105  and inverse non-linear transformation section  106 . 
     Time-frequency transformation processing section  101  applies a fast Fourier transform (FFT) to input signal x n  and finds a frequency component spectrum S 1 ( k ) (hereinafter “input spectrum”). 
     Then, time-frequency transformation processing section  101  outputs input spectrum S 1 ( k ) to subband dividing section  102 . 
     Subband dividing section  102  divides input spectrum S 1 ( k ) received as input from time-frequency transformation processing section  101 , into P subbands (where P is an integer equal to or greater than 2). Now, a case will be described below where subband dividing section  102  divides input spectrum S 1 ( k ) such that each subband contains the same number of samples. The number of samples may vary between subbands. Subband dividing section  102  outputs the spectrums divided per subband (hereinafter “subband spectrums”), to representative value calculating section  103 . 
     Representative value calculating section  103  calculates a representative value for each subband of an input spectrum divided into subbands, received as input from subband dividing section  102 , and outputs the representative value calculated per subband, to non-linear transformation section  104 . The processing in representative value calculating section  103  will be described in detail later. 
       FIG. 3  shows an inner configuration of representative value calculating section  103 . Representative value calculating section  103  shown in  FIG. 3  has arithmetic mean calculating section  201 , and geometric mean calculating section  202 . 
     First, subband dividing section  102  outputs a subband spectrum to arithmetic mean calculating section  201 . 
     Arithmetic mean calculating section  201  divides each subband of the subband spectrum received as input into Q subgroups of subgroup 0, subgroup Q−1, etc. (where Q is an integer equal to or greater than 2). Now, a case will be described below where Q subgroups are each formed with R samples (R is an integer equal to or greater than 2). Although a case will be described below where Q subgroups are all formed with R samples, the number of samples may vary between subgroups. 
       FIG. 4  shows a sample configuration of subbands and subgroups.  FIG. 4  shows, as an example, a case where the number of samples to constitute one subband is eight, the number of subgroups Q to constitute one subband is two and the number of samples R in one subgroup is four. 
     Next, for each of the Q subgroups, arithmetic mean calculating section  201  calculates an arithmetic mean of the absolute values of the spectrums (FFT coefficients) contained in each subgroup, using equation 1. 
                   (     Equation   ⁢           ⁢   1     )                               AVE   ⁢           ⁢     1   q       =       1   R     ⁢       ∑     i   =   0       R   -   1       ⁢           ⁢          S   ⁢           ⁢     1       BS   q     +   i                    ⁢     
     ⁢     (       q   =   0     ,       …   ⁢           ⁢   Q     -   1       )             [   1   ]               
In equation 1, AVE 1   q  is an arithmetic mean of the absolute values of the spectrums contained in subgroup q, and BS q  is the index of the leading sample in subgroup q.
 
     Next, arithmetic mean calculating section  201  outputs arithmetic mean value spectrums calculated per subband, AVE 1   q  (q=0˜Q−1) (subband arithmetic mean value spectrums), to geometric mean calculating section  202 . 
     Geometric mean calculating section  202  multiplies arithmetic mean value spectrums AVE 1   q  (q=0˜Q−1) of all subbands received as input from arithmetic mean calculating section  201 , as shown in equation 2, and calculates a representative spectrum, AVE 2   p  (p=0˜P−1), for each subband. 
                   (     Equation   ⁢           ⁢   2     )                               AVE   ⁢           ⁢     2   p       =       ∏     i   =   0       Q   -   1       ⁢           ⁢     AVE   ⁢           ⁢     1   i           ⁢     
     ⁢     (       p   =   0     ,       …   ⁢           ⁢   P     -   1       )             [   2   ]               
In equation 2, P is the number of subbands.
 
     Next, geometric mean calculating section  202  outputs calculated subband representative value spectrums AVE 2   p  (p=0˜P−1) to non-linear transformation section  104 . 
     Non-linear transformation section  104  applies non-linear transformation having a characteristic of emphasizing greater representative values, to subband representative value spectrums AVE 2   p , received as input from geometric mean calculating section  202 , using equation 3, and calculates first subband logarithmic representative value spectrums, AVE 3   p  (p=0˜P−1). A case will be described here where logarithmic transform is performed as non-linear transformation processing.
 
[3]
 
 AVE 3 p =log 10 ( AVE 2 p )( p= 0 , . . . P− 1)  (Equation 3)
 
     Next, a second subband logarithmic representative value spectrum, AVE 4   p  (p=0˜P−1), is calculated by multiplying calculated first subband logarithmic representative value spectrum, AVE 3   p  (p=0˜P−1) by the reciprocal of the number of subgroups, Q, using equation 4. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       AVE 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         4 
                         p 
                       
                     
                     = 
                     
                       
                         AVE 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           p 
                         
                       
                       Q 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         p 
                         = 
                         0 
                       
                       , 
                       
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           P 
                         
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   4 
                   ] 
                 
               
             
           
         
       
     
     Although in the processing of equation 2 in geometric mean calculating section  202  subband arithmetic mean value spectrums AVE 1   p  of individual subbands are simply multiplied, in the processing of equation 4 in non-linear transformation section  104 , a geometric mean is calculated. With the present embodiment, transformation into the logarithmic domain is performed using equation 3, and then multiplication by the reciprocal of the number of subgroups, Q, is performed using equation 4. By this means, radical root calculation, which involves a large amount of calculation, can be replaced by simple division. Furthermore, when the number of subgroups, Q, is a constant, the radical root calculation can be replaced by simple multiplication, by calculating the reciprocal of Q in advance, so that the amount of calculation can be reduced further. 
     Next, non-linear transformation section  104  outputs second subband logarithmic representative value spectrums AVE 4   9  (p=0˜P−1) calculated using equation 4, to smoothing section  105 . 
     Referring back to  FIG. 2  again, smoothing section  105  smoothes second subband logarithmic representative value spectrums AVE 4   p  (p=0˜P−1) received as input from non-linear transformation section  104 , in the frequency domain, using equation 5, and calculates logarithmic smoothed spectrums AVE 5   p  (p=0˜P−1). 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     AVE 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       5 
                       p 
                     
                   
                   = 
                   
                     
                       1 
                       MA_LEN 
                     
                     · 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           
                             p 
                             - 
                             
                               
                                 MA_LEN 
                                 - 
                                 1 
                               
                               2 
                             
                           
                         
                         
                           p 
                           + 
                           
                             
                               MA_LEN 
                               - 
                               1 
                             
                             2 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         AVE 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             4 
                             i 
                           
                           · 
                           
                               
                               
                           
                         
                         ⁢ 
                         
                           
                             W 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   MA_LEN 
                                   - 
                                   1 
                                 
                                 2 
                               
                               ≤ 
                               p 
                               ≤ 
                               
                                 P 
                                 - 
                                 1 
                                 - 
                                 
                                   
                                     MA_LEN 
                                     - 
                                     1 
                                   
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
           
         
       
     
     Equation 5 represents smoothing filtering processing, and, in this equation 5, MA_LEN is the order of smoothing filtering and W i  is the smoothing filter weight. 
     Furthermore, in equation 5 provides a method of calculating a logarithmic smoothed spectrum when subband index p is p&gt;=(MA_LEN−1)/2 and p&lt;=P−1−(MA_LEN−1)/2. When subband index p is at the top or near the last, spectrums are smoothed using equation 6 and equation 7 taking into account the boundary conditrions. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       6 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     AVE 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       5 
                       p 
                     
                   
                   = 
                   
                     
                       1 
                       
                         p 
                         + 
                         
                           
                             MA_LEN 
                             - 
                             1 
                           
                           2 
                         
                         + 
                         1 
                       
                     
                     · 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         
                           p 
                           + 
                           
                             
                               MA_LEN 
                               - 
                               1 
                             
                             2 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         AVE 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             4 
                             i 
                           
                           · 
                           
                             
                               W 
                               i 
                             
                             ⁡ 
                             
                               ( 
                               
                                 0 
                                 ≤ 
                                 p 
                                 &lt; 
                                 
                                   
                                     MA_LEN 
                                     - 
                                     1 
                                   
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       7 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     AVE 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       5 
                       p 
                     
                   
                   = 
                   
                     
                       1 
                       
                         P 
                         - 
                         1 
                         - 
                         p 
                         + 
                         
                           
                             MA_LEN 
                             - 
                             1 
                           
                           2 
                         
                         + 
                         1 
                       
                     
                     · 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           
                             p 
                             - 
                             
                               
                                 MA_LEN 
                                 - 
                                 1 
                               
                               2 
                             
                           
                         
                         
                           P 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         AVE 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             4 
                             i 
                           
                           · 
                           
                             
                               W 
                               i 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   P 
                                   - 
                                   1 
                                   - 
                                   
                                     
                                       MA_LEN 
                                       - 
                                       1 
                                     
                                     2 
                                   
                                 
                                 &lt; 
                                 p 
                                 ≤ 
                                 
                                   P 
                                   - 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   7 
                   ] 
                 
               
             
           
         
       
     
     Furthermore, smoothing section  105  performs smoothing based on simple moving average, as smoothing processing by smoothing filtering processing, as described above (when W i  is 1 for all i&#39;s, smoothing is performed based on moving average). For the window function (weight), Hanning window or other window functions may be used. 
     Next, smoothing section  105  outputs calculated smoothed spectrums AVE 5   p  (p=0˜P−1) to inverse non-linear transformation section  106 . 
     Inverse non-linear transformation section  106  performs inverse logarithmic transformation as inverse non-linear transformation for logarithmic smoothed spectrums AVE 5   p  (p=0˜P−1) received as input from smoothing section  105 . Inverse non-linear transformation section  106  performs inverse logarithmic transformation for logarithmic smoothed spectrums AVE 5   p  (p=0˜P−1) using equation 8, and calculates smoothed spectrum AVE 6   p  (p=0˜P−1).
 
[8]
 
 AVE 6 p =10 AVE5     p   ( p= 0 , . . . P− 1)  (Equation 8)
 
     Furthermore, inverse non-linear transformation section  106  calculates a smoothed spectrum of all samples using the values of samples in each subband as the values of linear domain smoothed spectrum AVE 6   p  (p=0˜P−1). 
     Inverse non-linear transformation section  106  outputs the smoothed spectrum values of all samples as a processing result of spectrum smoothing apparatus  100 . 
     The spectrum smoothing apparatus and spectrum smoothing method according to the present invention have been described. 
     As described above, with the present embodiment, subband dividing section  102  divides an input spectrum into a plurality of subbands, representative value calculating section  103  calculates representative value per subband using an arithmetic mean or geometric mean, non-linear transformation section  104  performs non-linear transformation having a characteristic of emphasizing greater values to each representative value, and smoothing section  105  smoothes representative values subjected to non-linear transformation per subband in the frequency domain. 
     Thus, all samples of a spectrum are divided into a plurality of subbands, and, for each subband, a representative value is found by combining an arithmetic mean with multiplication calculation or geometric mean, and then smoothing is performed after the representative value is subjected to non-linear transformation, so that it is possible to maintain good speech quality and reduce the amount of calculation processing substantially. 
     As described above, the present invention employs a configuration for calculating representative values of subbands by combining arithmetic means and geometric means of samples in subbands, so that it is possible to prevent speech quality degradation that can occur due to the variation of the scale of sample values in a subband when average values in the linear domain are used simply as representative values of subbands. 
     Although the fast Fourier transform (FFT) has been explained as an example of time-frequency transformation processing with the present embodiment, the present invention is by no means limited to this, and other time-frequency transformation methods besides the fast Fourier transform (FFT) are equally applicable. For example, according to patent literature 1, upon calculation of perceptual masking values (see  FIG. 2 ), the modified discrete cosine transform (MDCT), not the fast Fourier transform (FFT), is used to calculate frequency components (spectrum). Thus, the present invention is applicable to configurations using the modified discrete cosine transform (MDCT) and other time-frequency transformation methods in a time-frequency transformation processing section. 
     In the configuration described above, geometric mean calculating section  202  multiplies an arithmetic mean value spectrum AVE 1   4  (q=0˜Q−1), and does not calculate radical roots. That is to say, strictly speaking, geometric mean calculating section  202  does not calculate geometric mean values, because, as explained above, in non-linear transformation section  104 , transformation into the logarithmic domain is performed using equation 3 as non-linear transformation processing and then multiplication by the reciprocal of the number of subgroups Q is performed using equation 4, so that it is possible to replace radical root calculation by simple division (multiplication) and consequently reduce the amount of calculation. 
     Consequently, the present invention is not necessarily limited to the above configuration. The present invention is equally applicable to, for example, a configuration for multiplying, in geometric mean calculating section  202 , arithmetic mean value spectrums AVE 1   9  (q=0˜Q−1) by the values of arithmetic mean value spectrums per subband, and then calculating a radical root of the number of subgroups and outputting the calculated radical root to non-linear transformation section  104  as subband representative value spectrums AVE 2   p  (p=0˜P−1). Either way, smoothing section  105  is able to acquire a representative value having been subjected to non-linear transformation, per subband. In this case, the calculation of equation 4 in non-linear transformation section  104  may be omitted. 
     A case has been described above with the present embodiment where a representative value of each subband is calculated by, first, calculating an arithmetic mean value of a subgroup, and next finding a geometric mean value of the arithmetic mean values of all subgroups in a subband. However, the present invention is by no means limited to this and is equally applicable to a case where, for example, the number of samples to constitute a subgroup is one, that is, a case where a geometric mean value of all samples in a subband is used as a representative value of the subband without calculating an arithmetic mean value of each subgroup. In this configuration again, as described above, rather than calculating an accurate geometric mean value, it is possible to calculate a geometric mean value in the logarithmic domain by performing non-linear transformation and then performing multiplication by the reciprocal of the number of subgroups. 
     In the above description, all samples in a subband have the same spectrum value in inverse non-linear transformation section  106 . However, the present invention is by no means limited to this, and it is equally possible to provide an inverse smoothing processing section after inverse non-linear transformation section  106  so that the inverse smoothing processing section may assign weight to samples in each subband and perform inverse smoothing processing. This inverse smoothing processing needs not be completely opposite to smoothing section  105 . 
     Although a case has been described with the above description where non-linear transformation section  104  performs inverse logarithmic transformation as inverse non-linear transformation processing and inverse non-linear transformation section  106  performs inverse logarithmic transformation as inverse non-linear transformation processing, this is by no means limiting, and it is equally possible to use power transform and others and perform inverse processing of non-linear transformation as inverse non-linear transformation processing. However, given that calculation of a radical root can be replaced by simple division (multiplication) by multiplying the reciprocal of the number of subgroups Q using equation 4, the fact that non-linear transformation section  104  performs logarithmic transform as non-linear transformation, should be credited for the reduction of the amount of calculation. Consequently, if processing that is different from logarithmic transform is performed as non-linear transformation processing, it is then equally possible to calculate a representative value per subband by calculating a geometric mean value of arithmetic mean values of subgroups and apply non-linear processing to the representative values. 
     Furthermore, as for the number of subbands and, the number of subgroups, if, for example, the sampling frequency of an input signal is 32 kHz and one frame is 20 msec long, that is, if an input signal is comprised of 640 samples, it is possible to, for example, set the number of subbands to eighty, the number of subgroups to two, the number of samples per subgroup to four, and the order of smoothing filtering to seven, for example. The present invention is by no means limited to this setting and is equally applicable to cases where different values are applied. 
     The spectrum smoothing apparatus and spectrum smoothing method according to the present invention are applicable to any and all of spectrum smoothing devices or components that perform smoothing in the spectral domain, including speech coding apparatus and speech coding method, speech decoding apparatus and speech decoding method, and speech recognition apparatus and speech recognition method. For example, although, with the bandwidth enhancement technique disclosed in patent literature 2, processing for calculating a spectral envelope from LPCs (Linear Predictive Coefficients), and, based on this calculated spectral envelope, removing the spectral envelope from the lower band spectrum, is used to calculate parameters for generating a higher band spectrum, it is equally possible to use a smoothed spectrum calculated by applying the spectrum smoothing method according to the present invention to a lower band spectrum instead of the spectral envelope used in spectral envelope removing processing in patent literature 2. 
     Furthermore, although a configuration has been explained with the present embodiment where an input spectrum S 1 ( k ) is divided into P subbands (where P is an integer equal to or greater than 2) all having the same number of samples, the present invention is by no means limited to this and is equally applicable to a configuration in which the number of samples varies between subbands. For example, a configuration is possible in which subbands are divided such that a subband on the lower band side has a smaller number of samples and a subband on the higher band side has a greater number of samples. Generally speaking, in human perception, frequency resolution decreases in the higher band side, so that more efficient spectrum smoothing is made possible with the above configuration. The same applies to subgroups to constitute each subband. Although a case has been described above with the present embodiment where Q subgroups are all formed with R samples, the present invention is by no means limited to this, and is equally applicable to configurations where subgroups are divided such that a subgroup on the lower band side has a smaller number of samples and a subgroup on the higher band side has a larger number of samples. 
     Although weighted moving average has been described as an example of smoothing processing with the present embodiment, the present invention is by no means limited to this and is equally applicable to various smoothing processing. For example, as described above, in a configuration in which the number of samples varies between subbands (that is, the number of samples increases in the higher band), it is possible to make the number of taps in a moving average filter not the same between the left and the right and increase the number of taps in the higher band. When the number of samples increases in subbands in the higher band, it is possible to perform perceptually more adequate smoothing processing by using a moving average filter having a small number of taps in the higher band side. The present invention is applicable to cases using a moving average filter that is asymmetrical between the left and the right and has a greater number of taps on the higher band side. 
     Embodiment 2 
     A configuration will be described now with the present embodiment where the spectrum smoothing processing explained with embodiment 1 is used in preparatory processing upon band enhancement coding disclosed in patent literature 2. 
       FIG. 5  is a block diagram showing a configuration of a communication system having a coding apparatus and decoding apparatus according to embodiment 2. In  FIG. 5 , the communication system has a coding apparatus and decoding apparatus that are mutually communicable via a transmission channel. The coding apparatus and decoding apparatus are usually mounted in a base station apparatus and communication terminal apparatus for use. 
     Coding apparatus  301  divides an input signal every N samples (where N is a natural number) and performs coding on a per frame basis using N samples as one frame. The input signal to be subject to coding is represented as x n  (n=0, . . . , N−1). n is the (n+1)-th signal component in the input signal divided every N samples. Input information having been subjected to coding (coded information) is transmitted to decoding apparatus  303  via transmission channel  302 . 
     Decoding apparatus  303  receives the coded information transmitted from coding apparatus  301  via transmission channel  302 , and, by decoding this, acquires an output signal. 
       FIG. 6  is a block diagram showing an inner principal-part configuration of coding apparatus  301 . If input signal sampling frequency is SR input , down-sampling processing section  311  down-samples the input signal sampling frequency from SR input  to SR base  (SR base &lt;SR input ), and outputs input signal after down-sampling to first layer coding section  312  as a down-sampled input signal. 
     First layer coding section  312  generates first layer coded information by encoding the down-sampled input signal received as input from down-sampling processing section  311 , using a speech coding method of a CELP (Code Excited Linear Prediction) scheme, and outputs the generated first layer coded information to first layer decoding section  313  and coded information integrating section  317 . 
     First layer decoding section  313  generates a first layer decoded signal by decoding the first layer coded information received as input from first layer coding section  312 , using, for example, a CELP speech decoding method, and outputs the generated first layer decoded signal to up-sampling processing section  314 . 
     Up-sampling processing section  314  up-samples the sampling frequency of the input signal received as input from first layer decoding section  313  from SR base  to SR input , and outputs the first layer decoded signal after up-sampling to time-frequency transformation processing section  315  as an up-sampled first layer decoded signal. 
     Delay section  318  gives a delay of a predetermined length, to the input signal. This delay is to correct the time delay in down-sampling processing section  311 , first layer coding section  312 , first layer decoding section  313 , and up-sampling processing section  314 . 
     Time-frequency transformation processing section  315  has buffer buf 1   n  and buf 2   11  (n=0, . . . , N−1) inside, and applies a modified discrete cosine transform (MDCT) to input signal x n  and up-sampled first layer decoded signal y n  received as input from up-sampling processing section  314 . 
     Next, the orthogonal transformation processing in time-frequency transformation processing section  315  will be described as to its calculation step and data output to internal buffers. 
     First, time-frequency transformation processing section  315  initializes buf 1   n  and buf 2   n  using the initial value “0” according to equation 9 and equation 10 below.
 
[9]
 
buf1 n =0( n= 0 , . . . , N− 1)  (Equation 9)
 
[10]
 
buf2 n =0( n= 0 , . . . , N= 1)  (Equation 10)
 
     Next, time-frequency transformation processing section  315  performs an MDCT of input signal x n  and up-sampled first layer decoded signal y n , and finds MDCT coefficient S 2 ( k ) of the input signal (hereinafter “input spectrum”) and MDCT coefficient S 1 ( k ) of up-sampled first layer decoded signal y n  (hereinafter “first layer decoded spectrum”). 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         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 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   11 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         2 
                         N 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             
                               2 
                               ⁢ 
                               N 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             y 
                             n 
                             ′ 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         k 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   π 
                                 
                                 
                                   4 
                                   ⁢ 
                                   N 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         k 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         N 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   12 
                   ] 
                 
               
             
           
         
       
     
     K is the index of each sample in a frame. Time-frequency transformation processing section  315  finds x n ′, which is a vector combining input signal x n  and buffer bun1 n  from equation 13 below. Time-frequency transformation processing section  315  also finds y n ′ which is a vector combining up-sampled first layer decoded signal y n  and buffer buf 2   n . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     x 
                     n 
                     ′ 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             buf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               1 
                               n 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 0 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             x 
                             
                               n 
                               - 
                               N 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 N 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   13 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     y 
                     n 
                     ′ 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             buf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               2 
                               n 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 0 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             y 
                             
                               n 
                               - 
                               N 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 n 
                                 = 
                                 N 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   14 
                   ] 
                 
               
             
           
         
       
     
     Next, time-frequency transformation processing section  315  updates buffer buf 1   n  and buf 2   n  using equation 15 and equation 16.
 
[15]
 
buf1 n   =x   n ( n= 0 , . . . N− 1)  (Equation 15)
 
[16]
 
buf2 n   =y   n ( n= 0 , . . . N− 1)  (Equation 16)
 
     Then, time-frequency transformation processing section  315  outputs input spectrum S 2 ( k ) and first layer decoded spectrum S 1 ( k ) to second layer coding section  316 . 
     Second layer coding section  316  generates second layer coded information using input spectrum S 2 ( k ) and first layer decoded spectrum S 1 ( k ) received as input from time-frequency transformation processing section  315 , and outputs the generated second layer coded information to coded information integrating section  317 . The details of second layer coding section  316  will be described later. 
     Coded information integrating section  317  integrates the first layer coded information received as input from first layer coding section  312  and the second layer coded information received as input from second layer coding section  316 , and, if necessary, attaches a transmission error correction code to the integrated information source code, and outputs the result to transmission channel  302  as coded information. 
     Next, the inner principal-part configuration of second layer coding section  316  shown in  FIG. 6  will be described using  FIG. 7 . 
     Second layer coding section  316  has band dividing section  360 , spectrum smoothing section  361 , filter state setting section  362 , filtering section  363 , search section  364 , pitch coefficient setting section  365 , gain coding section  366  and multiplexing section  367 , and these sections perform the following operations. 
     Band dividing section  360  divides the higher band part (FL&lt;=k&lt;FH) of input spectrum S 2 ( k ) received as input from time-frequency transformation processing section  315  into P subbands SB p  (p=0, 1, . . . , P−1). Then, band dividing section  360  outputs bandwidth. BW p  (p=0, 1, . . . , P−1) and leading index BS p  (p=0, 1, . . . , P−1) (FL&lt;=BS p &lt;FH) of each divided subband to filtering section  363 , search section  364  and multiplexing section  367  as band division information. The part in input spectrum S 2 ( k ) corresponding to subband SB p  will be referred to as subband spectrum S 2   p (k) (BS p &lt;=k&lt;BS p +BW p ). 
     Spectrum smoothing section  361  applies smoothing processing to first layer decoded spectrum S 1 ( k ) (0&lt;=k&lt;FL) received as input from time-frequency transformation processing section  315 , outputs smoothed first layer decoded spectrum S 1 ′( k ) (0&lt;=k&lt;FL) after smoothing processing, to filter state setting section  362 . 
       FIG. 8  shows an internal configuration of spectrum smoothing section  361 . Spectrum smoothing section  361  is primarily configured with subband dividing section  102 , representative value calculating section  103 , non-linear transformation section  104 , smoothing section  105 , and inverse non-linear transformation section  106 . These components are the same as the components described with embodiment 1 and will be assigned the same reference numerals without explanations. 
     Filter state setting section  362  sets smoothed first layer decoded spectrum S 1 ′( k ) (0&lt;=k&lt;FL) received as input from spectrum smoothing section  361  as the internal filter state to use in subsequent filtering section  363 . Smoothed first layer decoded spectrum S 1 ′( k ) is accommodated as the internal filter state (filter state) in the 0&lt;=k&lt;FL band of spectrum S(k) over the entire frequency range in filtering section  363 . 
     Filtering section  363 , having a multi-tap pitch filter, filters the first layer decoded spectrum based on the filter state set in filter state setting section  362 , the pitch coefficient received as input from pitch coefficient setting section  365  and band division information received as input from band dividing section  360 , and calculates estimated spectrum S 2   p ′(k) (BS p &lt;=k&lt;BS p +BW p ) (p=0, 1, . . . , P−1) of each subband SB p  (p=0, 1, . . . , P−1) (hereinafter “subband SB p  estimated spectrum”). Filtering section  363  outputs estimated spectrum S 2   p ′(k) of subband SB p  to search section  364 . The details of filtering processing in filtering section  363  will be described later. The number of multiple taps may be any value (integer) equal to or greater than 1. 
     Based on band division information received as input from band dividing section  360 , search section  364  calculates the degree of similarity between estimated spectrum S 2   p ′(k) of subband SB p  received as input from filtering section  363 , and each subband spectrum S 2   p (k) in the higher band (FL&lt;=k&lt;FH) of input spectrum S 2 ( k ) received as input from time-frequency transformation processing section  315 . This degree of similarity is calculated by, for example, correlation calculation. Processing in filtering section  363 , search section  364  and pitch coefficient setting section  365  constitute closed-loop search processing per subband, and, in every closed loop, search section  364  calculates the degree of similarity with respect to each pitch coefficient by variously modifying pitch coefficient T received as input from pitch coefficient setting section  365  into filtering section  363 . In each subband&#39;s closed loop, or, for example, in a closed loop corresponding to subband SB p , search section  364  finds optimal pitch coefficient T p ′ to maximize the degree of similarity (in the range of Tmin˜Tmax), and outputs P optimal pitch coefficients to multiplexing section  367 . Search section  364  calculates part of the band of first layer decoded spectrum to resemble each subband SB p  using each optimal pitch coefficient T p ′. Then, search section  364  outputs estimated spectrum S 2   p ′(k) corresponding to each optimal pitch coefficient T p ′ (p=0, 1, . . . , P−1), to gain coding section  366 . The details of search processing for optimal pitch confident T p ′ (p=0, 1, . . . , P−1) in search section  364  will be described later. 
     Based on control by search section  364 , when pitch coefficient setting section  365  performs closed-loop search processing corresponding to first subband SB 0  with filtering section  363  and search section  364 , modifies pitch coefficient T gradually in a predetermined search range between Tmin and Tmax and sends outputs to filtering section  363  sequentially. 
     Gain coding section  366  calculates gain information with respect to higher band part (FL&lt;=k&lt;FH) of input spectrum S 2 ( k ) received as input from time-frequency transformation processing section  315 . To be more specific, gain coding section  366  divides frequency band FL&lt;=k&lt;FH into J subbands, and finds spectral power of input spectrum S 2 ( k ) per subband. In this case, spectral power B j  of the (j+1)-th subband is represented by equation 17 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       B 
                       j 
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             BL 
                             j 
                           
                         
                         
                           BH 
                           j 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         S 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           
                             ( 
                             k 
                             ) 
                           
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   17 
                   ] 
                 
               
             
           
         
       
     
     In equation 17, BL j  is the minimum frequency of the (j+1)-th subband, and BH j  is the maximum frequency of the (j+1)-th subband. Gain coding section  366  forms estimated spectrum S 2 ′( k ) of the higher band of input spectrum by connecting estimated spectrum S 2   p ′(k) (p=0, 1, . . . , P−1) of each subband received as input from search section  364  continue in the frequency domain. Then, gain coding section  366  calculates spectral power B′ j  of estimated spectrum S 2 ′( k ) per subband, as in the case of calculating the spectral power of input spectrum S 2 ( k ), using equation 18 below. Next, gain coding section  366  calculates the amount of variation, V j , of the spectral power of estimated spectrum S 2 ′( k ) per subband, with respect to input spectrum S 2 ( k ), using equation 19 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       B 
                       j 
                       ′ 
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             BL 
                             j 
                           
                         
                         
                           BH 
                           j 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         S 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           ′ 
                         
                         ⁢ 
                         
                           
                             ( 
                             k 
                             ) 
                           
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   18 
                   ] 
                 
               
             
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       V 
                       j 
                     
                     = 
                     
                       
                         
                           B 
                           j 
                         
                         
                           B 
                           j 
                           ′ 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         j 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         J 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   19 
                   ] 
                 
               
             
           
         
       
     
     Then, gain coding section  366  encodes amount of variation V j , and outputs an index corresponding to coded amount of variation VQ j  to multiplexing section  367 . 
     Multiplexing section  367  multiplexes band division information received as input from band dividing section  360 , optimal pitch coefficient T p ′ for each subband SB p  (p=0, 1, . . . , P−1) received as input from search section  364 , and an index of variation amount VQ j  received as input from gain coding section  366 , as second layer coded information, and outputs that second layer coded information to coded information integrating section  317 . It is equally possible to input T p ′ and the index of VQ j  directly in coded information integrating section  317 , and multiplex these with first layer coded information in coded information integrating section  317 . 
     The details of filtering processing in filtering section  363  shown in  FIG. 7  will be described in detail using  FIG. 9 . 
     Using the filter state received as input from filter state setting section  362 , pitch coefficient T received as input from pitch coefficient setting section  365 , and band division information received as input from band dividing section  360 , filtering section  363  generates an estimated spectrum in band BS p &lt;=k&lt;BS p +BW p  (p=0, 1, . . . , P−1) of subband SB p  (p=0, 1, . . . , P−1). The transfer function F(z) of the filter used in filtering section  363  is represented by equation 20 below. 
     Now, using SB p  as an example, the process of generating estimated spectrum S 2   p ′(k) of subband spectrum S 2   p (k) will be explained. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     F 
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       1 
                       - 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             
                               - 
                               M 
                             
                           
                           M 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             β 
                             i 
                           
                           ⁢ 
                           
                             z 
                             
                               
                                 - 
                                 T 
                               
                               + 
                               i 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   20 
                   ] 
                 
               
             
           
         
       
     
     In equation 20, T is a pitch coefficient provided from pitch coefficient setting section  365 , and β i  is a filter coefficient stored inside in advance. For example, when the number of taps is three, filter coefficient candidates include (β −1 , β 0 , β 1 )=(0.1, 0.8, 0.1), for example. 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. Values (β −1 , β 0 , β 1 )=(0.0, 1.0, 0.0) are also applicable, and, in this case, part of the band 0&lt;=k&lt;FL of first layer decoded spectrum is not modified in shape and copied as is in the band of BS p &lt;=k&lt;BS p +BW p . M=1 in equation 20. M is an indicator related to the number of taps. 
     Smoothed first layer decoded spectrum S 1 ′( k ) is accommodated in the 0&lt;=k&lt;FL band of spectrum S(k) of the entire frequency band in filtering section  363  as the internal filter state (filter state). 
     In the BS p &lt;=k&lt;BS p +BW p  band of S(k), estimated spectrum S 2   p ′(k) of subband SB p  is accommodated by filtering processing of the following steps. Basically, in S 2   p ′(k), spectrum S(k−T) having a frequency T lower than this k, is substituted. To improve the smoothness of a spectrum, in practice, spectrum β i ·S(k−T+i) given by multiplying nearby spectrum S(k−T+i) that is i apart from spectrum S(k−T) by predetermined filter coefficient β i  is found with respect to all i&#39;s, and a spectrum adding the spectrums of all i&#39;s is substituted in S 2   p ′(k). This processing is represented by equation 21 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       2 
                       p 
                       ′ 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           - 
                           1 
                         
                       
                       1 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           β 
                           i 
                         
                         · 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         
                           ( 
                           
                             k 
                             - 
                             T 
                             + 
                             i 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   21 
                   ] 
                 
               
             
           
         
       
     
     Estimated spectrum S 2   p ′(k) in BS p &lt;=k&lt;BS p +BW p  is calculated by performing the above calculation in order from the lowest frequency and changing k in the range of BS p &lt;=k&lt;BS p +BW p . 
     The above filtering processing is performed by zero-clearing S(k) in the range BS p &lt;=k&lt;BS p +BW p  every time pitch coefficient T is provided from pitch coefficient setting section  365 . 
     That is to say, S(k) is calculated every time pitch coefficient T changes and outputted to search section  364 . 
       FIG. 10  is a flowchart showing the steps of processing for searching for optimal pitch coefficient T p ′ for subband SB p  in search section  364 . Search section  364  searches for optimal pitch coefficient T p ′ (p=0, 1, . . . , P−1) in each subband SB p  (p=0, 1, . . . , P−1) by repeating the steps shown in  FIG. 10 . 
     First, search section  364  initializes the minimum degree of similarity, D min , which is a variable for saving the minimum value of the degree of similarity, to “+8” (ST  110 ). Next, following equation 22 below, at a given pitch coefficient, search section  364  calculates the degree of similarity, D, between the higher band part (FL&lt;=k&lt;FH) of input spectrum S 2 ( k ) and estimated spectrum S 2   p ′(k) (ST  120 ). 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       22 
                     
                     ) 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     D 
                     = 
                     
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             M 
                             ′ 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           S 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   BS 
                                   p 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                             · 
                             S 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 BS 
                                 p 
                               
                               + 
                               k 
                             
                             ) 
                           
                         
                       
                       - 
                       
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   M 
                                   ′ 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 S 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       
                                         BS 
                                         p 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   · 
                                   S 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   2 
                                   ′ 
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       BS 
                                       p 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               M 
                               ′ 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               2 
                               ′ 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     BS 
                                     p 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                               · 
                               S 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               2 
                               ′ 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   BS 
                                   p 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         0 
                         &lt; 
                         
                           M 
                           ′ 
                         
                         ≤ 
                         
                           BW 
                           p 
                         
                       
                       ) 
                     
                     . 
                   
                 
               
               
                 
                   [ 
                   22 
                   ] 
                 
               
             
           
         
       
     
     In equation 22, M′ is the number of samples upon calculating the degree of similarity D, and may assume arbitrary values equal to or smaller than the bandwidth of each subband. S 2   p ′(k) is not present in equation 22 but is represented using BS p  and S 2 ′( k ). 
     Next, search section  364  determines whether or not the calculated degree of similarity, D, is smaller than the minimum degree of similarity, D min  (ST  130 ). If degree of similarity D calculated in ST  120  is smaller than minimum degree of similarity D min  (“YES” in ST  130 ), search section  364  substitutes degree of similarity D in minimum degree of similarity D min  (ST  140 ). On the other hand, if degree of similarity D calculated in ST  120  is equal to or greater than minimum degree of similarity D min  (“NO” in ST  130 ), search section  364  determines whether or not processing in the search range has finished. That is to say, search section  364  determines whether or not the degree of similarity has been calculated with respect to all pitch coefficients in the search range in ST  120  according to equation 22 above (ST  150 ). Search section  364  returns to ST  120  again when the processing has not finished over the search range (“NO” in ST  150 ). Then, search section  364  calculates the degree of similarity according to equation 22, for different pitch coefficients from the case of calculating the degree of similarity according to equation 22 in earlier ST  120 . On the other hand, when processing is finished over the search range (“YES” in ST  150 ), search section  364  outputs pitch coefficient T corresponding to the minimum degree of similarity, to multiplexing section  367 , as optimal pitch coefficient T p ′ (ST  160 ). 
     Next, decoding apparatus  303  shown in  FIG. 5  will be described. 
       FIG. 11  is a block diagram showing an internal principal-part configuration of decoding apparatus  303 . 
     In  FIG. 11 , coded information demultiplexing section  331  demultiplexs between first layer coded information and second layer coded information in coded information received as input, outputs the first layer coded information to first layer decoding section  332 , and outputs the second layer coded information to second layer decoding section  335 . 
     First layer decoding section  332  decodes the first layer coded information received as input from coded information demultiplexing section  331 , and outputs the generated first layer decoded signal to up-sampling processing section  333 . The operations of first layer decoding section  332  are the same as in first layer decoding section  313  shown in  FIG. 6  and will not be explained in detail. 
     Up-sampling processing section  333  performs processing of up-sampling the sampling frequency from SR base  to SR input  with respect to the first layer decoded signal received as input from first layer decoding section  332 , and outputs the resulting up-sampled first layer decoded signal to time-frequency transformation processing section  334 . 
     Time-frequency transformation processing section  334  applies orthogonal transformation processing (MDCT) to the up-sampled first layer decoded signal received as input from up-sampling processing section  333 , and outputs the MDCT coefficient S 1 ( k ) (hereinafter “first layer decoded spectrum”) of the resulting up-sampled first layer decoded signal to second layer decoding section  335 . The operations of time-frequency transformation processing section  334  are the same as the processing in time-frequency transformation processing section  315  for an up-sampled first layer decoded signal shown in  FIG. 6 , and will not be described in detail. 
     Second layer decoding section  335  generates a second layer decoded signal including higher band components using first layer decoded spectrum S 1 ( k ) received as input from time-frequency transformation processing section  334  and second layer coded information received as input from coded information demultiplexing section  331 , and outputs this as an output signal. 
       FIG. 12  is a block diagram showing an internal principal-part configuration of second layer decoding section  335  shown in  FIG. 11 . 
     Demultiplexing section  351  demultiplexes the second layer coded information received as input from coded information demultiplexing section  331  into band division information including bandwidth BW p  (p=0, 1, . . . , P−1) and leading index BS P  (p=0, 1, . . . , P−1) (FL&lt;=BS p &lt;FH) of each subband, optimal pitch coefficient T p ′ (p=0, 1, . . . , P−1), which is information related to filtering, and the index of coded amount of variation VQ j  (j=0, 1, . . . , J−1), which is information related to gain. Furthermore, demultiplexing section  351  outputs band division information and optimal pitch coefficient T p ′ (p=0, 1, . . . , P−1) to filtering section  354 , and outputs the index of coded amount of variation VQ j  (j=0, 1, . . . , J−1) to gain decoding section  355 . If in coded information demultiplexing section  331  band division information T p ′ (p=0, 1, . . . , P−1) and VQ j  (j=0, J−1) index are demultiplexed, demultiplexing section  351  is not necessary. 
     Spectrum smoothing section  352  applies smoothing processing to first layer decoded spectrum S 1 ( k ) (0&lt;=k&lt;FL) received as input from time-frequency transformation processing section  334 , and outputs smoothed first layer decoded spectrum S 1 ′( k ) (0&lt;=k&lt;FL) to filter state setting section  353 . The processing in spectrum smoothing section  352  is the same as the processing in spectrum smoothing section  361  in second layer coding section  316  and therefore will not be described here. 
     Filter state setting section  353  sets smoothed first layer decoded spectrum S 1 ′( k ) (0&lt;=k&lt;FL) received as input from spectrum smoothing section  352  as the filter state to use in filtering section  354 . Calling the spectrum of the entire 0&lt;=k&lt;FH frequency band “S(k)” in filtering section  354  for convenience, smoothed first layer decoded spectrum S 1 ′( k ) is accommodated in the 0&lt;=k&lt;FL band of S(k) as the internal filter state (filter state). The configuration and operations of filter state setting section  353  are the same as filter state setting section  362  shown in  FIG. 7  and will not be described in detail here. 
     Filtering section  354  has a multi-tap pitch filter (having at least two taps). Filtering section  354  filters smoothed first layer decoded spectrum S 1 ′( k ) based on band division information received as input from demultiplexing section  351 , the filter state set in filter state setting section  353 , pitch coefficient T p ′ (p=0, 1, . . . , P−1) received as input from demultiplexing section  351 , and a filter coefficient stored inside in advance, and calculates estimated spectrum S 2   p ′(k) (BS p &lt;=k&lt;BS p +BW p ) (p=0, 1, . . . , P−1) of each subband SB p  (p=0, . . . , P−1) shown in equation 21 above. Filtering section  354  also uses the filter function represented by equation 20. The filtering processing and filter function in this case are represented as in equation 20 and equation 21 except that T is replaced by T p ′. 
     Gain decoding section  355  decodes the index of coded variation amount VQ j  received as input from demultiplexing section  351 , and finds amount of variation VQ j  which is a quantized value of amount of variation V j . 
     Spectrum adjusting section  356  finds estimated spectrum S 2 ′( k ) of an input spectrum by connecting estimated spectrum S 2   p ′(k) (BS p &lt;=k&lt;BS p +BW p ) (p=0, 1, . . . , P−1) of each subband received as input from filtering section  354  in the frequency domain. According to equation 23 below, spectrum adjusting section  356  furthermore multiplies estimated spectrum S 2 ′( k ) by amount of variation VQ j  of each subband received as input from gain decoding section  355 . By this means, spectrum adjusting section  356  adjust the spectral shape in the FL&lt;=k&lt;FH frequency band of estimated spectrum S 2 ′( k ), generates decoded spectrum S 3 ( k ) and outputs decoded spectrum S 3 ( k ) to time-frequency transformation processing section  357 .
 
[23]
 
 S 3( k )= S 2′( k )· VQ   j ( BL   j   ≦k≦BH   j , for all  j )  (Equation 23)
 
     Next, according to equation 24, spectrum adjusting section  356  substitutes first layer decoded spectrum S 1 ( k ) (0&lt;=k&lt;FL), received as input from time-frequency transformation processing section  334 , in the low band (0&lt;=k&lt;FL) of decoded spectrum S 3 ( k ). 
     The lower band part (0&lt;=k&lt;FL) of decoded spectrum S 3 ( k ) is formed with first layer decoded spectrum S 1 ( k ) and the higher band part (FL&lt;=k&lt;FH) of decoded spectrum S 3 ( k ) is formed with estimated spectrum S 2 ′( k ) after the spectral shape adjustment.
 
[24]
 
 S 3( k )= S 1( k )(0 ≦k≦FL )  (Equation 24)
 
     Time-frequency transformation processing section  357  performs orthogonal transformation of decoded spectrum S 3 ( k ) received as input from spectrum adjusting section  356  into a time domain signal, and outputs the resulting second layer decoded signal as an output signal. Here, if necessary, adequate processing such as windowing or overlap addition is performed to prevent discontinuities from being produced between frames. 
     The processing in time-frequency transformation processing section  357  will be described in detail. 
     Time-frequency transformation processing section  357  has buffer buf′(k) inside and initializes buffer buf′(k) as shown with equation 25 below.
 
[25]
 
buf′( k )=0( k= 0 , . . . , N− 1)  (Equation 25)
 
     Furthermore, according to equation 26 below, time-frequency transformation processing section  357  finds second layer decoded signal y n ″ using second layer decoded spectrum S 3 ( k ) received as input from spectrum adjusting section  356 . 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       n 
                       ″ 
                     
                     = 
                     
                       
                         2 
                         N 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             
                               2 
                               ⁢ 
                               N 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Z 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                           ⁢ 
                           
                             ( 
                             k 
                             ) 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         k 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   π 
                                 
                                 
                                   4 
                                   ⁢ 
                                   N 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         n 
                         = 
                         0 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         N 
                         - 
                         1 
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   26 
                   ] 
                 
               
             
           
         
       
     
     In equation 26, Z 4 ( k ) is a vector combining decoded spectrum S 3 ( k ) and buffer buf′(k) as shown by equation 27 below. 
     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Z 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               buf 
                               
                                 
                                     
                                 
                                 ⁢ 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 k 
                                 = 
                                 0 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             S 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 k 
                                 = 
                                 N 
                               
                               , 
                               
                                 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   27 
                   ] 
                 
               
             
           
         
       
     
     Next, time-frequency transformation processing section  357  updates buffer buf′(k) according to equation 28 below.
 
[28]
 
buf′( k )= S 3( k )( k= 0 , . . . N− 1)  (Equation 28)
 
     Next, time-frequency transformation processing section  357  outputs decoded signal y n ″ as an output signal. 
     Thus, according to the present embodiment, in coding/decoding for performing bandwidth enhancement using a lower band spectrum and estimating a higher band spectrum, smoothing processing to combine an arithmetic mean and geometric mean is performed for a lower band spectrum as preparatory processing. By this means, it is possible to reduce the amount of calculation without causing quality degradation of a decoded signal. 
     Furthermore, although a configuration has been explained above with the present embodiment where, upon bandwidth enhancement coding, a lower band decoded spectrum obtained by means of decoding is subjected to smoothing processing and a higher band spectrum is estimated using a smoothed lower band decoded spectrum and coded, the present invention is by no means limited to this and is equally applicable to a configuration for performing smoothing processing for a lower band spectrum of an input signal, estimating a higher band spectrum from a smoothed input spectrum and then coding the higher band spectrum. 
     The spectrum smoothing apparatus and spectrum smoothing method according to the present invention are by no means limited to the above embodiments and can be implemented in various modifications. For example, embodiments may be combined in various ways. 
     The present invention is equally applicable to cases where a signal processing program is recorded or written in a computer-readable recording medium such as a CD and DVD and operated, and provides the same working effects and advantages as with the present embodiment. 
     Although example cases have been described above with the above embodiments where the present invention is implemented with hardware, the present invention can be implemented with software as well. 
     Furthermore, each function block employed in the above descriptions of embodiments may typically be implemented as an LSI constituted by an integrated circuit. These may be individual chips or partially or totally contained on a single chip. “LSI” is adopted here but this may also be referred to as “IC,” “system LSI,” “super LSI,” or “ultra LSI” depending on differing extents of integration. 
     Further, the method of circuit integration is not limited to LSI&#39;s, and implementation using dedicated circuitry or general purpose processors is also possible. After LSI manufacture, utilization of an FPGA (Field Programmable Gate Array) or a reconfigurable processor where connections and settings of circuit cells in an LSI can be regenerated is also possible. 
     Further, if integrated circuit technology comes out to replace LSI&#39;s as a result of the advancement of semiconductor technology or a derivative other technology, it is naturally also possible to carry out function block integration using this technology. Application of biotechnology is also possible. 
     The disclosures of Japanese Patent Application No. 2008-205645, filed on Aug. 8, 2008, Japanese Patent Application No, 2009-096222, filed on Apr. 10, 2009, including the specifications, drawings and abstracts, are incorporated herein by reference in their entireties. 
     INDUSTRIAL APPLICABILITY 
     The spectrum smoothing apparatus, coding apparatus, decoding apparatus, communication terminal apparatus, base station apparatus and spectrum smoothing method according to the present invention make possible smoothing in the frequency domain by a small of amount and are therefore applicable to, for example, packet communication systems, mobile communication systems and so forth. 
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Explanation of Reference Numerals 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 100  
                 Spectrum smoothing apparatus 
               
               
                   
                 101, 315,  
                 Time-frequency transformation  
               
               
                   
                 334, 357 
                 processing section 
               
               
                   
                 102  
                 Subband dividing section 
               
               
                   
                 103  
                 Representative value calculating section 
               
               
                   
                 104  
                 Non-linear transformation section 
               
               
                   
                 105 
                 Smoothing section 
               
               
                   
                 106 
                 Inverse non-linear transformation section 
               
               
                   
                 201 
                 Arithmetic mean calculating section 
               
               
                   
                 202  
                 Geometric mean calculating section 
               
               
                   
                 301 
                 Coding apparatus 
               
               
                   
                 302 
                 Transmission channel 
               
               
                   
                 303 
                 Decoding apparatus 
               
               
                   
                 311 
                 Down-sampling processing section 
               
               
                   
                 312 
                 First layer coding section 
               
               
                   
                 313, 332 
                 First layer decoding section 
               
               
                   
                 314, 333 
                 Up-sampling processing section 
               
               
                   
                 316 
                 Second layer coding section 
               
               
                   
                 317 
                 Coded information integrating section 
               
               
                   
                 318 
                 Delay section 
               
               
                   
                 331 
                 Coded information demultiplexing section 
               
               
                   
                 335 
                 Second layer decoding section 
               
               
                   
                 351 
                 Demultiplexing section 
               
               
                   
                 352, 361 
                 Spectrum smoothing section 
               
               
                   
                 353, 362 
                 Filter state setting section 
               
               
                   
                 354, 363 
                 Filtering section 
               
               
                   
                 355 
                 Gain coding section 
               
               
                   
                 356 
                 Spectrum adjusting section 
               
               
                   
                 360 
                 Band dividing section 
               
               
                   
                 364 
                 Search section 
               
               
                   
                 365 
                 Pitch coefficient setting section 
               
               
                   
                 366 
                 Gain coding section 
               
               
                   
                 367 
                 Multiplexing section