Patent Publication Number: US-9837085-B2

Title: Audio encoding device and audio coding method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2013-241522 filed on Nov. 22, 2013, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments discussed herein are related to, for example, audio encoding devices, audio coding methods, audio coding programs, and audio decoding devices. 
     BACKGROUND 
     Audio signal coding methods of compressing the data amount of a multi-channel audio signal having three or more channels have been developed. As one of such coding methods, the MPEG Surround method standardized by Moving Picture Experts Group (MPEG) is known. Outline of the MPEG Surround method is disclosed, for example, in a MPEG Surround Specification: ISO/IEC23003-1. In the MPEG Surround method, for example, an audio signal of 5.1 channels (5.1 ch) to be encoded is subjected to time-frequency transformation, and a frequency signal thus obtained through time-frequency transformation is downmixed and thereby a three-channel frequency signal is generated once. Further, the three-channel frequency signal is downmixed again to calculate a frequency signal corresponding to a two-channel stereo signal. Then, the frequency signal corresponding to the stereo signal is encoded by the Advanced Audio Coding (MC) coding method, and the Spectral band replication (SBR) coding method. On the other hand, in the MPEG Surround method, when 5.1 channel signal is downmixed to produce a three-channel signal and the three channel signal is downmixed to produce a two channel signal, spatial information representing sound spread or localization is calculated and then encoded. In such a manner, the MPEG Surround method encodes a stereo signal generated by downmixing a multi-channel audio signal and spatial information having relatively less data amount. Thus, the MPEG Surround method provides compression efficiency higher than the efficiency obtained by independently coding signals of channels contained in the multi-channel audio signal. 
     In the MPEG Surround method, the three-channel frequency signal is encoded by dividing into a stereo frequency signal and two predictive coefficients (channel prediction coefficients) in order to reduce the amount of encoded information. The predictive coefficient is a coefficient for predictively coding a signal of one of three channels based on signals of other two channels. A plurality of predictive coefficients are stored in a table called the codebook, which is used for improving the efficiency of bits to be used. With an encoder and a decoder having a common predetermined codebook (or a codebook prepared in a common way), important information can be sent with less number of bits. When encoding, a predictive coefficient is selected from the codebook. When decoding, a signal of one of three channels is reproduced based on the selected predictive coefficient. 
     SUMMARY 
     In accordance with an aspect of the embodiments, an audio encoding device includes a processor; and a memory which stores a plurality of instructions, which when executed by the processor, cause the processor to execute: calculating a similarity in phase of a first channel signal and a second channel signal contained in a plurality of channels of an audio signal; and selecting, based on the similarity, a first output that outputs one of the first channel signal and the second channel signal, or a second output that outputs both of the first channel signal and the second channel signal. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       These and/or other aspects and advantages will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawing of which: 
         FIG. 1  is a functional block diagram of an audio encoding device according to one embodiment. 
         FIG. 2  is a diagram illustrating an example of a quantization table (codebook) relative to a predictive coefficient. 
         FIG. 3A  is a conceptual diagram of a plurality of first samples contained in a first channel signal. 
         FIG. 3B  is a conceptual diagram of a plurality of second samples contained in a second channel signal. 
         FIG. 3C  is a conceptual diagram of amplitude ratios of the first sample and the second sample. 
         FIG. 4  is a diagram illustrating an example of a quantization table relative to a similarity. 
         FIG. 5  is an example of a diagram illustrating the relationship between an index differential value and similarity code. 
         FIG. 6  is a diagram illustrating an example of a quantization table relative to an intensity difference. 
         FIG. 7  is a diagram illustrating an example of a data format in which an encoded audio signal is stored. 
         FIG. 8  is an operation flow chart of audio coding processing. 
         FIG. 9A  is a spectrum diagram of an original sound of the multi-channel audio signal. 
         FIG. 9B  is a spectrum diagram of a decoded audio signal subjected to a coding according to Embodiment 1. 
         FIG. 10  is a diagram illustrating the coding efficiency subjected to an audio coding according to Embodiment 1. 
         FIG. 11  is a functional block diagram of an audio decoding device according to one embodiment. 
         FIG. 12  is a functional block diagram (Part 1) of an audio encoding/decoding system according to one embodiment. 
         FIG. 13  is a functional block diagram (Part 2) of an audio encoding/decoding system according to one embodiment. 
         FIG. 14  is a hardware configuration diagram of a computer functioning as an audio encoding device or an audio decoding device according to one embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of an audio encoding device, an audio coding method and an audio coding computer program as well as an audio decoding device are described in detail with reference to the accompanying drawings. Embodiments do not limit the disclosed art. 
     (Embodiment 1) 
       FIG. 1  is a functional block diagram of an audio encoding device  1  according to one embodiment. As illustrated in  FIG. 1 , the audio encoding device  1  includes a time-frequency transformation unit  11 , a first downmix unit  12 , a predictive encoding unit  13 , a second downmix unit  14 , a calculation unit  15 , a selection unit  16 , a channel signal encoding unit  17 , a spatial information encoding unit  21 , and a multiplexing unit  22 . 
     Further, the channel signal encoding unit  17  includes a Spectral band replication (SBR) encoding unit  18 , a frequency-time transformation unit  19 , and an Advanced Audio Coding (MC) encoding unit  20 . 
     Those components included in the audio encoding device  1  are formed as separate hardware circuits using wired logic, for example. Alternatively, those components included in the audio encoding device  1  may be implemented into the audio encoding device  1  as one integrated circuit in which circuits corresponding to respective components are integrated. The integrated circuit may be an integrated circuit such as, for example, an application specific integrated circuit (ASIC) and a field programmable gate array (FPGA). Further, these components included in the audio encoding device  1  may be function modules which are achieved by a computer program implemented on a processor included in the audio encoding device  1 . 
     The time-frequency transformation unit  11  is configured to transform signals of the respective channels in the time domain of multi-channel audio signals entered to the audio encoding device  1  to frequency signals of the respective channels by time-frequency transformation on the frame by frame basis. In this embodiment, the time-frequency transformation unit  11  transforms signals of the respective channels to frequency signals by using a Quadrature Mirror Filter (QMF) filter bank of the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       QMF 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
                           n 
                         
                         ) 
                       
                     
                     = 
                     
                       exp 
                       ⁡ 
                       
                         [ 
                         
                           j 
                           ⁢ 
                           
                             π 
                             128 
                           
                           ⁢ 
                           
                             ( 
                             
                               k 
                               + 
                               0.5 
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 n 
                               
                               + 
                               1 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     0 
                     ≤ 
                     k 
                     &lt; 
                     64 
                   
                   , 
                   
                     0 
                     ≤ 
                     n 
                     &lt; 
                     128 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, “n” is a variable representing an nth time of the audio signal in one frame divided clockwise into 128 parts. The frame length may be, for example, any value between 10 and 80 msec. “k” is a variable representing a kth frequency band of the frequency signal divided into 64 parts. QMF(k,n) is QMF for providing a frequency signal having the time “n” and the frequency “k”. The time-frequency transformation unit  11  generates a frequency signal of a channel by multiplying QMF (k,n) by an audio signal for one frame of the entered channel. The time-frequency transformation unit  11  may transform signals of the respective channels to frequency signals through another time-frequency transformation processing such as fast Fourier transform, discrete cosine transform, and modified discrete cosine transform. 
     Every time calculating the signals on the frame by frame basis, the time-frequency transformation unit  11  outputs frequency signals of the respective channels to the first downmix unit  12 . 
     Every time receiving frequency signals from the time-frequency transformation unit  11 , the first downmix unit  12  generates left-channel, center-channel and right-channel frequency signals by downmixing the frequency signals of the respective channels. For example, the first downmix unit  12  calculates frequency signals of the following three channels in accordance with the following equation.
 
 L   in ( k,n )= L   inRe ( k,n )+ j·L   inIm ( k,n )0≦ k&lt; 64,0≦ n&lt; 128
 
 L   inRe ( k,n )= L   Re ( k,n )+ SL   Re ( k,n )
 
 L   inIm ( k,n )= L   Im ( k,n )+ SL   Im ( k,n )
 
 R   in ( k,n )= R   inRe ( k,n )+ j·R   inIm ( k,n )0≦ k&lt; 64,0≦ n&lt; 128
 
 R   inRe ( k,n )= R   Re ( k,n )+ SR   Re ( k,n )
 
 R   inIM ( k,n )= R   Im ( k,n )+ SR   Im ( k,n )
 
 C   in ( k,n )= C   inRe ( k,n )+ j·C   inIm ( k,n )0≦ k&lt; 64,0≦ n&lt; 128
 
 C   inRe ( k,n )= C   Re ( k,n )+ LFE   Re ( k,n )
 
 C   inIm ( k,n )= C   Im ( k,n )+ LFE   Im ( k,n )  (Equation 2)
 
     Here, L Re (k,n) represents a real part of the left front channel frequency signal L(k,n), and L Im (k,n) represents an imaginary part of the left front channel frequency signal L(k,n). SL Re (k,n) represents a real part of the left rear channel frequency signal SL(k,n), and SL Im (k,n) represents an imaginary part of the left rear channel frequency signal SL(k,n). L in (k,n) is a left-channel frequency signal generated by downmixing. L inRe (k,n) represents a real part of the left-channel frequency signal, and L inIm (k,n) represents an imaginary part of the left-channel frequency signal. 
     Similarly, R Re (k,n) represents a real part of the right front channel frequency signal R(k,n), and R Im (k,n) represents an imaginary part of the right front channel frequency signal R(k,n). S RRe (k,n) represents a real part of the right rear channel frequency signal SR(k,n), and SR Im (k,n) represents an imaginary part of the right rear channel frequency signal SR(k,n). R in (k,n) is a right-channel frequency signal generated by downmixing. R inRe (k,n) represents a real part of the right-channel frequency signal, and R inIm (k,n) represents an imaginary part of the right-channel frequency signal. 
     Further, C Re (k,n) represents a real part of the center-channel frequency signal C(k,n), and C Im (k,n) represents an imaginary part of the center-channel frequency signal C(k,n). LFE Re (k,n) represents a real part of the deep bass sound channel frequency signal LFE(k,n), and LFE Im (k,n) represents an imaginary part of the deep bass sound channel frequency signal LFE(k,n). C in (k,n) is a center-channel frequency signal generated by downmixing. Further, C inRe (k,n) represents a real part of the center-channel frequency signal C in (k,n), and C inIm (k,n) represents an imaginary part of the center-channel frequency signal C in (k,n). 
     The first downmix unit  12  calculates, on the frequency band basis, an intensity difference between frequency signals of two downmixed channels, and a similarity between the frequency signals, as spatial information between the frequency signals. The intensity difference is information representing the sound localization, and the similarity becomes information representing the sound spread. The spatial information calculated by the first downmix unit  12  is an example of three-channel spatial information. In this embodiment, the first downmix unit  12  calculates an intensity difference CLD L (k) and a similarity ICC L (k) in a frequency band k of the left channel in accordance with the following equations. 
     
       
         
           
             
               
                 
                   
                     
                       CLD 
                       L 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     10 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         log 
                         10 
                       
                       ( 
                       
                         
                           
                             e 
                             L 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         
                           
                             e 
                             SL 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         ICC 
                         L 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             
                               e 
                               LSL 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             
                               
                                 
                                   e 
                                   L 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               · 
                               
                                 
                                   e 
                                   SL 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         L 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             L 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         SL 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             SL 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         LSL 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           L 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               , 
                               n 
                             
                             ) 
                           
                         
                         · 
                         
                           SL 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               , 
                               n 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, “N” represents the number of clockwise samples contained in one frame. In this embodiment, “N” is 128. e L (k) represents an autocorrelation value of the left front channel frequency signal L(k,n), and e SL (k) is an autocorrelation value of the left rear channel frequency signal SL(k,n). e LSL (k) represents a cross-correlation value between the left front channel frequency signal L(k,n) and the left rear channel frequency signal SL(k,n). 
     Similarly, the first downmix unit  12  calculates an intensity difference CLD R (k) and a similarity ICC R (k) of a frequency band k of the right-channel in accordance with the following equations. 
     
       
         
           
             
               
                 
                   
                     
                       CLD 
                       R 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     10 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         log 
                         10 
                       
                       ( 
                       
                         
                           
                             e 
                             R 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         
                           
                             e 
                             SR 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         ICC 
                         R 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       Re 
                       ⁢ 
                       
                         { 
                         
                           
                             
                               e 
                               RSR 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             
                               
                                 
                                   e 
                                   R 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               · 
                               
                                 
                                   e 
                                   SR 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         R 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             R 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         SR 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             SR 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         RSR 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           L 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               , 
                               n 
                             
                             ) 
                           
                         
                         · 
                         
                           SR 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               , 
                               n 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, e R (k) represents an autocorrelation value of the right front channel frequency signal R(k,n), and e SR (k) is an autocorrelation value of the right rear channel frequency signal SR(k,n). e RSR (k) represents a cross-correlation value between the right front channel frequency signal R(k,n) and the right rear channel frequency signal SR(k,n). 
     Further, the first downmix unit  12  calculates an intensity difference CLD c (k) in a frequency band k of the center-channel in accordance with the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       
                         CLD 
                         C 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       10 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           log 
                           10 
                         
                         ( 
                         
                           
                             
                               e 
                               C 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             
                               e 
                               LFE 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         C 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             C 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         e 
                         LFE 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             LFE 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, e C (k) represents an autocorrelation value of the center-channel frequency signal C(k,n), and e LFE (k) is an autocorrelation value of deep bass sound channel frequency signal LFE(k,n). 
     The first downmix unit  12  generates the three channel frequency signal and then further generates a left frequency signal in the stereo frequency signal by downmixing the left-channel frequency signal and the center-channel frequency signal. The second downmix unit  14  generates a right frequency signal in the stereo frequency signal by downmixing the right-channel frequency signal and the center-channel frequency signal. The first downmix unit  12  generates, for example, a left frequency signal L 0 (k,n) and a right frequency signal R 0 (k,n) in the stereo frequency signal in accordance with the following equation. Further, the first downmix unit  12  calculates, for example, a center-channel signal C 0 (k,n) utilized for selecting a predictive coefficient contained in the codebook. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               L 
                               0 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               R 
                               0 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               C 
                               0 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             
                               
                                 2 
                               
                               2 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             
                               
                                 2 
                               
                               2 
                             
                           
                         
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             
                               - 
                               
                                 
                                   2 
                                 
                                 2 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 L 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   n 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 R 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   n 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 C 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   n 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, L in (k,n), R in (k,n), and C in (k,n) are respectively left-channel, right-channel, and center-channel frequency signals generated by the first downmix unit  12 . The left frequency signal L 0 (k,n) is a synthesis of the left front channel, left rear channel, center-channel, and deep bass sound frequency signals of the original multi-channel audio signal. Similarly, the right frequency signal R 0 (k,n) is a synthesis of the right front channel, right rear channel, center-channel and deep bass sound frequency signals of the original multi-channel audio signal. 
     The first downmix unit  12  outputs the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the center-channel signal C 0 (k,n) to the predictive encoding unit  13  and the second downmix unit  14 . The first downmix unit  12  outputs the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n) to the calculation unit  15 . Further, the first downmix unit  12  outputs intensity differences CLD L (k), CLD R (k) and CLD R (k) and similarities ICC R (k) and ICC R (k), both serving as spatial information, to the spatial information encoding unit  21 . The left frequency signal L o (k,n) and the right frequency signal R o (k,n) in Equation 8 may be expanded as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         L 
                         0 
                       
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
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                     = 
                     
                       
                         ( 
                         
                           
                             
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                                 ⁢ 
                                 
                                     
                                 
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                             ⁡ 
                             
                               ( 
                               
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                           + 
                           
                             
                               
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                             ⁢ 
                             
                               
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                                   ⁢ 
                                   
                                       
                                   
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                               ⁡ 
                               
                                 ( 
                                 
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                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             
                               L 
                               
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                                 ⁢ 
                                 
                                     
                                 
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                               ( 
                               
                                 k 
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                               ) 
                             
                           
                           + 
                           
                             
                               
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                                   ⁢ 
                                   
                                       
                                   
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                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
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                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         R 
                         0 
                       
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
                           n 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               R 
                               
                                 in 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Re 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 2 
                               
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                             ⁢ 
                             
                               
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                                   in 
                                   ⁢ 
                                   
                                       
                                   
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                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   , 
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                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             
                               R 
                               
                                 in 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Im 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 , 
                                 n 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               
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                             ⁢ 
                             
                               
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                                   ⁢ 
                                   
                                       
                                   
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                                 ( 
                                 
                                   k 
                                   , 
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                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     The second downmix unit  14  receives the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the center-channel signal C 0 (k,n) from the first downmix unit  12 . The second downmix unit  14  downmixes two frequency signals out of the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the center-channel signal C 0 (k,n) received from the first downmix unit  12  to generate a stereo frequency signal of two channels. For example, the stereo frequency signal of two channels is generated from the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n). Then, the second downmix unit  14  outputs the stereo frequency signal to the selection unit  16 . 
     The predictive encoding unit  13  receives the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the central frequency signal C 0 (k,n) from the first downmix unit  12 . The predictive encoding unit  13  selects predictive coefficients from the codebook for frequency signals of two channels downmixed by the second downmix unit  14 . For example, when performing predictive coding of the center-channel signal C 0 (k,n) from the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n), the second downmix unit  14  generates a two-channel stereo frequency signal by downmixing the right frequency signal R o (k,n) and the left frequency signal L 0 (k,n). When performing predictive coding, the predictive encoding unit  13  selects, from the codebook, predictive coefficients c 1  (k) and c 2 (k) such that an error d(k,n) between a frequency signal before predictive coding and a frequency signal after predictive coding becomes minimum (or a value less than any predetermined second threshold, which may be 0.5), the error being defined on the frequency band basis in the following equations with C 0 (k,n), L 0 (k,n), and R 0 (k,n). In such a manner, the predictive encoding unit  13  performs predictive coding of the center-channel signal C′ 0 (k,n) subjected to predictive coding. 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
                           n 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         k 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           n 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           { 
                           
                             
                                
                               
                                 
                                   
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                                     0 
                                   
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                                     ( 
                                     
                                       k 
                                       , 
                                       n 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     C 
                                     0 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       , 
                                       n 
                                     
                                     ) 
                                   
                                 
                               
                                
                             
                             2 
                           
                           } 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       C 
                       0 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       
                         k 
                         , 
                         n 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           c 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       · 
                       
                         
                           L 
                           0 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             , 
                             n 
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         
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                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       · 
                       
                         
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                           0 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             , 
                             n 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     Equation  10  may be expressed as follows by using real and imaginary parts.
 
C′ 0 (k,n)=C′ oRe (k,n)+C′ 0Im (k,n)
 
[[C′ 0Re (k,n)=c 1 ×L 0Re (k,n)+c 2 ×R 0Re (k,n)]]
 
[[C′ 0Im (k,n)=c 1 ×L 0Im (k,n)+c 2 ×R 0Im (k,n)]]
 
C′ 0Re (k,n)=C 1 (k)×L 0Re (k,n)+C 2 (k)×R 0Re (k,n)
 
C′ 0Im (k,n)=c 1 (k)×L 0Im (k,n)+c 2 (k)×R 0Im (k,n)  (Equation 11)
 
     L 0Re (k,n), L 0Im (k,n), R 0Re (k,n), and R 0Re (k,n) represent a real part of L 0 (k,n), an imaginary part of L 0 (k,n), a real part of R 0 (k,n), and an imaginary part of R 0 (k,n) respectively. 
     As described above, the predictive encoding unit  13  can perform predictive coding of the center-channel signal C 0 (k,n) by selecting, from the codebook, predictive coefficients c 1 (k) and c 2 (k) such that the error d(k,n) between a center-channel frequency signal C′ 0 (k,n) before predictive coding and a center-channel frequency signal C′ 0 (k,n) after predictive coding becomes minimum. Equation 10 represents this concept in the form of the equation. 
     By using predictive coefficients c 1 (k) and c 2 (k) contained in the codebook, the predictive encoding unit  13  refers to a quantization table (codebook) illustrating a correspondence relationship between representative values of predictive coefficients c 1 (k) and c 2 (k) held by the predictive encoding unit  13 , and index values. Then, the predictive encoding unit  13  determines index values most close to predictive coefficients c 1 (k) and c 2 (k) for respective frequency bands by referring to the quantization table. Here, a specific example is described.  FIG. 2  is a diagram illustrating an example of the quantization table (codebook) relative to the predictive coefficient. In the quantization table  200  illustrated in  FIG. 2 , fields in rows  201 ,  203 ,  205 ,  207  and  209  represent index values. On the other hand, fields in rows  202 ,  204 ,  206 , and  208  respectively represent representative values corresponding to index values in fields of rows  201 ,  203 ,  205 ,  207 , and  209  in same rows. For example, when the predictive coefficient c 1 (k) relative to the frequency band k is 1.2, the second downmix unit  13  sets the index value relative to the predictive coefficient c 1 (k) to 12. 
     Next, the predictive encoding unit  13  determines a differential value between indexes in the frequency direction for frequency bands. For example, when an index value relative to a frequency band k is 2 and an index value relative to a frequency band (k−1) is 4, the predictive encoding unit  13  determines that the differential value of the index relative to the frequency band k is −2. 
     The predictive encoding unit  13  refers to, for example, the a-coding table 200 illustrating a correspondence relationship between the index-to-index differential value and the predictive coefficient code. Then, the predictive encoding unit  13  determines a predictive coefficient code index idxc m (k)(m=1,2 or m=1) of the predictive coefficient c m (k)(m=1,2 or m=1) relative to a differential value of frequency bands k by referring to the coding table 200. Like the similarity code, the predictive coefficient code can be a variable length code having a shorter code length for a differential value of higher appearance frequency, such as, for example, the Huffman coding or the arithmetic coding. The quantization table and the coding table are stored in advance in an unillustrated memory in the predictive encoding unit  13 . In  FIG. 1 , the predictive encoding unit  13  outputs the predictive coefficient code idxc m (k)(m=1,2) to the spatial information encoding unit  21 . 
     In the above method for selecting the predictive coefficient from the codebook, a plurality of predictive coefficients c 1 (k) and c 2 (k) may be included in the codebook such that an error d(k,n) between a frequency signal yet subjected to the predictive coding and a frequency signal subjected to the predictive coding becomes minimum (or less than any predetermined second threshold), for example, as disclosed in Japanese Laid-open Patent Publication No. 2013-148682). In this case, the predictive encoding unit  13  outputs any number of sets of predictive coefficients c 1 (k) and c 2 (k), and as appropriate, the number of predictive coefficients c 1 (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any predetermined second threshold). 
     The calculation unit  15  receives the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n) from the first downmix unit  12 . The calculation unit  15  also receives the number of predictive coefficients c 1 (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any predetermined second threshold), from the predictive encoding unit  13 , as appropriate. The calculation unit  15  calculates a similarity in phase between the first channel signal and the second channel signal contained in a plurality of channels of the audio signal, as a first calculation method of the similarity in phase. Specifically, the calculation unit  15  calculates a similarity in phase between the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n). The calculation unit  15  also calculates a similarity in phase based on the number of predictive coefficients with which an error in the predictive coding of a third channel signal contained in a plurality of channels of the audio signal becomes less than the above second threshold, as a second calculation method of the similarity in phase. Specifically, the calculation unit  15  calculates the similarity based on the number of predictive coefficients c 1 (k) and c 2 (k) received from the predictive encoding unit  13 . The third channel signal corresponds to, for example, the center-channel signal C 0 (k,n). Hereinafter, the first calculation method and the second calculation method of the similarity in phase by the calculation unit  15  are described in detail. 
     (First Calculation Method of Similarity in Phase) 
     The calculation unit  15  calculates a similarity in phase based on an amplitude ratio between a plurality of first samples contained in a first channel signal and a plurality of second samples contained in a second channel signal. Specifically, the calculation unit  15  determines the similarity in phase, for example, based on an amplitude ratio between a plurality of first samples contained in the left frequency signal L 0 (k,n) as an example of the first channel signal and a plurality of second samples contained in the right frequency signal R 0 (k,n) as an example of the second channel signal. Technical significance of the similarity in phase is described later.  FIG. 3A  is a conceptual diagram of a plurality of first samples contained in the first channel signal.  FIG. 3B  is a conceptual diagram of a plurality of second samples contained in the second channel signal.  FIG. 3C  is a conceptual diagram of an amplitude ratio between the first sample and the second sample. 
       FIG. 3A  illustrates an amplitude relative to a given time of the left frequency signal L 0 (k,n) as an example of the first channel signal, in which the left frequency signal L 0 (k,n) contains a plurality of first samples.  FIG. 3B  illustrates an amplitude relative to a given time of the right frequency signal R 0 (k,n) as an example of the second channel signal, in which the right frequency signal R 0 (k,n) contains a plurality of second samples. The calculation unit  15  calculates, for example, an amplitude ratio p between the first sample and the second sample at a given time t which is a same time within a predetermined time range, according to the following equation.
 
 p=l   0t   /r   0t   (Equation 12)
 
     In Equation 12, l 0t  represents amplitude of the first sample at time t, and r 0t  represents amplitude of the second sample at the time t. 
     Here, technical significance of the similarity in phase is described. In  FIG. 3C , an amplitude ratio between the first sample and the second sample relative to the time t calculated by the calculation unit  15  is illustrated. The selection unit  16  described later determines, for example, whether the amplitude ratio p of respective samples contained in a frame on the frame by frame basis at time t is less than a predetermined threshold (which may be called a third threshold). For example, if amplitude ratios p of all samples (or amplitude ratio p of any fixed number of samples) are less than a predetermined third threshold (for example, the third threshold may be 0.095 or more and less than 1.05), phases of the first channel signal and the second channel signal may be considered to be the same. In other words, when amplitude ratios p of all samples (or amplitude ratios of any fixed number of samples) are less than a predetermined third threshold, amplitudes of the first channel signal and the second channel signal are equal to each other. When phases of the first channel signal and the second channel signal are different from each other, amplitudes may different in many cases generally. Therefore, a substantial phase difference (similarity in phase) between the first channel signal and the second channel signal may be calculated by using the amplitude ratio p and the third threshold. Further by considering amplitude ratios p of all samples (or, amplitude ratios of any fixed number), an effect that a sample has a same amplitude ratio accidentally even when the phase is different can be excluded. For example, in the frame  2  illustrated in  FIG. 3C , when amplitude ratios of all samples (or, amplitude ratios of samples of any fixed number) are equal to or more than the third threshold, phases of the first channel signal and the second channel signal may be considered not to be the same. Further, for example, amplitude ratios of all samples p in respective frames or amplitude ratios of samples of any fixed number p may be referred to as a similarity in phase. The calculation unit  15  outputs the similarity in phase to the selection unit  16 . 
     (Second Calculation Method of Similarity in Phase) 
     The calculation unit  15  receives the number of predictive coefficients c l  (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any predetermined second threshold), from the predictive encoding unit  13 . When there are three or more sets of predictive coefficients c l  (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any fixed number of the second threshold), the left frequency signal L 0 (k,n) as an example of the first channel signal and the right frequency signal R 0 (k,n) as an example of the second channel signal may be considered to have a same phase in view of the nature of the vector computation expressed by Equation  10 . When there is one or two sets of predictive coefficients c l  (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any fixed number of the second threshold), the left frequency signal L 0 (k,n) as an example of the first channel signal and the right frequency signal R 0 (k,n) as an example of the second channel signal may be considered not to have a same phase. The number of sets of predictive coefficients c l  (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any fixed number of the second threshold) may be referred to as the similarity in phase. Since the second calculation method of the similarity in phase uses computation results of the predictive encoding unit  13  based on Equation  10 , the second calculation method can reduce computation load for computing the amplitude ratio p of samples and so on, in comparison with the first computation method. The calculation unit  15  outputs the similarity in phase to the selection unit  16 . 
     The selection unit  16  illustrated in  FIG. 1  receives the stereo frequency signal from the second downmix unit  14 . The selection unit  16  also receives the similarity in phase from the calculation unit  15 . The selection unit  16  selects, based on the similarity in phase, a first output that outputs either one of the first channel signal (for example, the left frequency signal L 0 (k,n)) and the second channel signal (for example, the right frequency signal R 0 (k,n)), or a second output that outputs both (the stereo frequency signal) of the first channel signal and the second channel signal. The selection unit  16  selects the first output when the similarity in phase is equal to or more than a predetermined first threshold, and selects the second output when the similarity in phase is less than the first threshold. 
     For example, when the calculation unit  15  calculates the similarity in phase based on the above first calculation method, the selection unit  16  can define the first threshold with the number of predictive coefficients with which amplitude ratios p of all samples in each frame or amplitude ratios p of any number of samples satisfy the above third threshold. In this case, the first threshold may be assumed, for example, to be 90%. Also, for example, when the calculation unit  15  calculates the similarity in phase based on the above second calculation method, the selection unit  16  can define the first threshold by using the number of sets of predictive coefficients c l  (k) and c 2 (k) with which error d(k,n) becomes minimum (or less than any predetermined second threshold). In this case, three sets of the first threshold (with six c l  (k) and c 2 (k)) may be defined, for example. 
     When selecting the first output, the selection unit  16  calculates spatial information of the first channel signal and the second channel signal, and outputs the spatial information to the spatial information encoding unit  21 . The spatial information may be, for example, a signal ratio between the first channel signal and the second channel signal. Specifically, the calculation unit  15  calculates an amplitude ratio p (which may be referred to as a signal ratio p) between the left frequency signal L.sub. 0 (k,n) and the right frequency signal R.sub. 0 (k,n) by using Equation  12  as spatial information. When the calculation unit  15  calculates the similarity in phase by using the above first calculation method, the selection unit  16  may receive the amplitude ratio p from the calculation unit  15  and output the amplitude ratio p to the spatial information encoding unit  21  as spatial information. Further, the selection unit  16  may output an average value pave of amplitude ratios of all samples in respective frames to the spatial information encoding unit  21  as spatial information. 
     The channel signal encoding unit  17  encodes a frequency signal(s) received from the selection unit  16  (a frequency signal of either one of the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n), or a stereo frequency signal of both of the left and right frequency signals). The channel signal encoding unit  17  includes a SBR encoding unit  18 , a frequency-time transformation unit  19 , and an MC encoding unit  20 . 
     Every time receiving a frequency signal, the SBR encoding unit  18  encodes a high-region component, which is a component contained in a high frequency band, out of the frequency signal on the channel by channel basis according to the SBR coding method. Thus, the SBR encoding unit  18  generates the SBR code. For example, the SBR encoding unit  18  replicates a low-region component of frequency signals of the respective channels having a strong correlation with a high-region component subjected to the SBR coding, as disclosed in Japanese Laid-open Patent Publication No. 2008-224902. The low-region component is a component of a frequency signal of the respective channels contained in a low frequency band lower than a high frequency band in which a high-region component to be encoded by the SBR encoding unit  18  is contained. The low-region component is encoded by the MC encoding unit  20  described later. Then, the SBR encoding unit  18  adjusts power of the replicated high-region component so as to match with power of the original high-region component. If it is not able to approximate a component in the original high-region component to a high-region component due to a significant difference from a low-region component even after replicating the low-region component, the SBR encoding unit  18  processes the component as auxiliary information. Then, the SBR encoding unit  18  encodes information representing a position relationship between a low-region component used for the replication and a high-region component, a power adjustment amount, and auxiliary information by quantizing. The SBR encoding unit  18  outputs a SBR code representing above encoded information to the multiplexing unit  22 . 
     Every time receiving a frequency signal, the frequency-time transformation unit  19  transforms the frequency signal of each channel to a time domain signal or a stereo signal. For example, when the time-frequency transformation unit  11  uses the QMF filter bank, the frequency-time transformation unit  19  performs frequency-time transformation of frequency signals of the respective channels by using a complex QMF filter bank indicated in the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       IQMF 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           , 
                           n 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         64 
                       
                       ⁢ 
                       
                         exp 
                         ⁡ 
                         
                           ( 
                           
                             j 
                             ⁢ 
                             
                               π 
                               128 
                             
                             ⁢ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 0.5 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   n 
                                 
                                 - 
                                 255 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     0 
                     ≤ 
                     k 
                     &lt; 
                     64 
                   
                   , 
                   
                     0 
                     ≤ 
                     n 
                     &lt; 
                     128 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, IQMF(k,n) is a complex QMF using the time “n” and the frequency “k” as variables. When the time-frequency transformation unit  11  uses another time-frequency transformation processing such as fast Fourier transform, discrete cosine transform, and modified discrete cosine transform, the frequency-time transformation unit  19  uses inverse transformation of the time-frequency transformation processing. The frequency-time transformation unit  19  outputs a stereo signal of the respective channels obtained by frequency-time transformation of the frequency signal of the respective channels to the MC encoding unit  20 . 
     Every time receiving a signal or a stereo signal of the respective channels, the MC encoding unit  20  generates an MC code by encoding a low-region component of respective channel signals according to the MC coding method. Here, the MC encoding unit  20  may utilize a technology disclosed, for example, in Japanese Laid-open Patent Publication No. 2007-183528. Specifically, the MC encoding unit  20  generates frequency signals again by performing the discrete cosine transform of the received stereo signals of the respective channels. Then, the MC encoding unit  20  calculates perceptual entropy (PE) from the re-generated frequency signal. The PE represents the amount of information for quantizing the block so that the listener (user) does not perceive noise. 
     The above PE is characterized in that it becomes greater with respect to a sound having a signal level varying sharply in a short time, such as, for example, an attack sound like a sound produced with a percussion instrument. Thus, the MC encoding unit  20  reduces the window length for a block having a relatively high PE value, and increases the window length for a block having a relatively low PE value. For example, the short window length contains 256 samples, and the long window length contains 2,048 samples. The MC encoding unit  20  performs the modified discrete cosine transform (MDCT) of signals or stereo signals of the respective channels by using a window having a predetermined length to transform the signals or stereo signals to a set of MDCT coefficients. Then, the MC encoding unit  20  quantizes the set of MDCT coefficients and performs variable-length coding of the set of quantized MDCT coefficients. The MC encoding unit  20  outputs the set of MDCT coefficients subjected to the variable-length coding and relevant information such as quantization coefficients to the multiplexing unit  22 , as the MC code. 
     The spatial information encoding unit  21  generates a MPEG Surround code (hereinafter, referred to as a MPS code) from spatial information received from the first downmix unit  12 , predictive coefficient codes received from the predictive encoding unit  13 , and spatial information received from the calculation unit  15 . 
     The spatial information encoding unit  21  refers to the quantization table illustrating a correspondence relationship between the similarity value and the index value in spatial information. Then, the spatial information encoding unit  21  determines an index value most close to each similarity ICC i (k)(i=L,R,0) for respective frequency bands by referring to the quantization table. The quantization table may be stored in advance in an unillustrated memory in the spatial information encoding unit  21 , and so on. 
       FIG. 4  is a diagram illustrating an example of a quantization table relative to a similarity. In a quantization table  400  illustrated in  FIG. 4 , each field in the upper row  410  represents an index value, and each field in the lower row  420  represents a representative value of the similarity corresponding to an index value in the same column. An acceptable value of the similarity is in the range between −0.99 and +1. For example, when the similarity relative to the frequency band k is 0.6, a representative value of a similarity corresponding to the index value  3  is most close to the similarity relative to the frequency band k in the quantization table  400 . Thus, the spatial information encoding unit  21  sets the index value relative to the frequency band k to 3. 
     Next, the spatial information encoding unit  21  determines a differential value between indexes in the frequency direction for frequency bands. For example, when an index value relative to a frequency band k is 3 and an index value relative to a frequency band (k−1) is 0, the spatial information encoding unit  21  determines that the differential value of the index relative to the frequency band k is 3. 
     The spatial information encoding unit  21  refers to a coding table illustrating a correspondence relationship between the differential value of indexes and the similarity code. Then, the spatial information encoding unit  21  determines the similarity code idxicc i (k)(i=L,R,0) of the similarity ICC i (k)(i=L,R,0) relative to the differential value between indexes for frequencies by referring to the coding table. The coding table is stored in advance in a memory in the spatial information encoding unit  21 , and so on. The similarity code can be a variable length code having a shorter code length for a differential value of higher appearance frequency, such as, for example, the Huffman coding or the arithmetic coding. 
       FIG. 5  is an example of a diagram illustrating the relationship between an index differential value and similarity code. In the example illustrated in  FIG. 5 , the similarity code is the Huffman coding. In a coding table  500  illustrated in  FIG. 5 , each field in the left row represents an index differential value, and each field in the right row represents a similarity code associated with an index differential value in a same column. For example, when an index differential value relative to a similarity ICC L (k) of a frequency band k is 3, the spatial information encoding unit  21  sets the similarity code idxicc L (k) relative to the similarity ICC L (k) of the frequency band k to “111110” by referring to the coding table  500 . 
     The spatial information encoding unit  21  refers to a quantization table illustrating a correspondence relationship between the intensity differential value and the index value. Then, the spatial information encoding unit  21  determines an index value most close to the intensity difference CLD j (k)(j=L,R,C,1,2) for respective frequency bands by referring to the quantization table. The spatial information encoding unit  21  determines a differential value between indexes in the frequency direction for frequency bands. For example, when an index value relative to a frequency band k is 2 and an index value relative to a frequency band (k−1) is 4, the spatial information encoding unit  21  determines that the differential value of the index relative to the frequency band k is −2. 
     The spatial information encoding unit  21  refers to a coding table illustrating a correspondence relationship between the index-to-index differential value and the intensity code. Then, the spatial information encoding unit  21  determines the intensity difference code idxcld j (k)(j=L,R,C,1,2) relative to the differential value of the intensity difference CLD j (k) for frequency bands k by referring to the coding table. The intensity difference code can be a variable length code having a shorter code length for a differential value of higher appearance frequency, such as, for example, the Huffman coding or the arithmetic coding. The quantization table and the coding table may be stored in advance in a memory in the spatial information encoding unit  21 . 
       FIG. 6  is a diagram illustrating an example of a quantization table relative to an intensity difference. In a quantization table  600  illustrated in  FIG. 6 , each field in rows  610 ,  630  and  650  represents an index value, and each field in rows  620 ,  640  and  660  represents a representative value of the intensity difference corresponding to an index value indicated in each field in rows  610 ,  630  and  650  of a same column. For example, when the intensity difference CLD L (k) relative to the frequency band k is 10.8 dB, a representative value of an intensity difference corresponding to the index value  5  is most close to CLD L (k) in the quantization table  600 . Thus, the spatial information encoding unit  21  sets the index value relative to CLD L(k)  to 5. 
     The spatial information encoding unit  21  generates the MPS code by using the similarity code idxicc i (k), the intensity difference code idxcld j (k), and the predictive coefficient code idxc m (k). For example, the spatial information encoding unit  21  generates the MPS code by arranging the similarity code idxicc i (k), the intensity difference code idxcld j (k), and the predictive coefficient code idxc m (k) in a predetermined sequence. The predetermined sequence is described, for example, in ISO/IEC23003-1:2007. The spatial information encoding unit  21  generates the MPS code by also arranging spatial information (amplitude ratio p) received from the selection unit  16 . The spatial information encoding unit  21  outputs the generated MPS code to the multiplexing unit  22 . 
     The multiplexing unit  22  multiplexes the MC code, the SBR code, and the MPS code by arranging in a predetermined sequence. Then, the multiplexing unit  22  outputs an encoded audio signal generated by multiplexing.  FIG. 7  is a diagram illustrating an example of a data format in which an encoded audio signal is stored. In the example illustrated in  FIG. 7 , the encoded audio signal is created in accordance with the MPEG-4 Audio Data Transport Stream (ADTS) format. In the encoded data string  700  illustrated in  FIG. 7 , the MC code is stored in the data block  710 . The SBR code and the MPS code are stored in a partial area of the block  720  in which a FILL element of the ADTS format is stored. The multiplexing unit  22  may store selection information indicating which output the selection unit  16  selects, the first output or the second output, in a partial portion of the block  720 . 
       FIG. 8  is an operation flow chart of audio coding. The flow chart illustrated in  FIG. 8  represents processing to the multi-channel audio signal corresponding to one frame. The audio encoding device  1  repeatedly implements audio coding steps illustrated in  FIG. 8  on the frame by frame basis while the multi-channel audio signal is being received. 
     The time-frequency transformation unit  11  transforms signals of the respective channels to frequency signals (step S 801 ). The time-frequency transformation unit  11  outputs time frequency signals of the respective channels to the first downmix unit  12 . 
     Then, the first downmix unit  12  generates the left-channel frequency L 0 (k,n), the right frequency signal R 0 (k,n), and the central frequency signal C 0 (k,n) by downmixing frequency signals of the respective channels. Further, the first downmix unit  12  calculates spatial information of right, left and center channels (step S 802 ). The first downmix unit  12  outputs frequency signals of the three channels to the predictive encoding unit  13  and the second downmix unit  14 . 
     The predictive encoding unit  13  receives frequency signals of the three channels including the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the central frequency signal C 0 (k,n) from the first downmix unit  12 . The predictive encoding unit  13  selects, from the codebook, predictive coefficients c 1 (k) and c 2 (k) with which the error d(k,n) between the downmixed two channel frequency signals, that is a frequency signal prior to predictive coding and a frequency signal after predictive coding, becomes minimum, by using Equation 10 (step S 803 ). The predictive encoding unit  13  outputs a predictive coefficient code idxc m (k)(m=1,2) corresponding to the predictive coefficients c 1 (k) and c 2 (k) to the spatial information encoding unit  21 . The predictive encoding unit  13  also outputs the number of sets of predictive coefficients c 1 (k) and c 2 (k) to the calculation unit  15 , as appropriate. 
     The calculation unit  15  receives the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n) from the first downmix unit  12 . The calculation unit  15  also receives the number of sets of predictive coefficients c 1 (k) and c 2 (k) with which the error d(k,n) becomes minimum (or, less than any predetermined second threshold), from the predictive encoding unit  13 , as appropriate. The calculation unit  15  calculates the similarity in phase by using the first calculation method or the second calculation method described above (step S 804 ). The calculation unit  15  outputs the similarity in phase to the selection unit  16 . 
     The selection unit  16  receives the stereo frequency signal from the second downmix unit  14 . The selection unit  16  also receives the similarity in phase from the calculation unit  15 . The selection unit  16  selects, based on the similarity in phase, a first output that outputs either one of the first channel signal (for example, the left frequency signal L 0 (k,n)) and the second channel signal (for example, the right frequency signal R 0 (k,n,)), or a second output that outputs both (the stereo frequency signal) of the first channel signal and the second channel signal (step S 805 ). When the similarity in phase is equal to or more than a predetermined first threshold (step S 805 —Yes), the selection unit  16  selects the first output (step S 806 ). When the similarity in phase is less than the first threshold (step S 805 —No), the selection unit selects the second output (step S 807 ). 
     When selecting the first output, the selection unit  16  calculates spatial information of the first channel signal and the second channel signal, and outputs the spatial information to the spatial information encoding unit  21  (step S 808 ). The spatial information may be, for example, an amplitude ratio between the first channel signal and the second channel signal. Specifically, the calculation unit  15  calculates an amplitude ratio p (which may be referred to as a signal ratio p) between the left frequency signal L.sub. 0 (k,n) and the right frequency signal R.sub. 0 (k,n) by using Equation  12  as spatial information. 
     The channel signal encoding unit  17  encodes a frequency signal(s) received from the selection unit  16  (a frequency signal of either one of the left frequency signal L 0 (k,n) and the right frequency signal R 0 (k,n), or a stereo frequency signal of both of the left and right frequency signals). For example, the channel signal encoding unit  17  performs SBR encoding of a high-region component in a frequency signal of respective received channels. Also, the channel signal encoding unit  17  performs AAC encoding of a low-region component not subjected to SBR encoding in a frequency signal of respective received channels (step S 809 ). Then, the channel signal encoding unit  17  outputs a SBR code and an MC code of information representing a positional relation between the low-region component used for replication and the corresponding high-region component, to the multiplexing unit  22 . 
     The spatial information encoding unit  21  generates a MPS code from spatial information for encoding received from the first downmix unit  12 , predictive coefficient codes received from the predictive encoding unit  13 , and spatial information received from the calculation unit  15  (step S 810 ). The spatial information encoding unit  21  outputs the generated MPS code to the multiplexing unit  22 . 
     Finally, the multiplexing unit  22  generates an encoded audio signal by multiplexing the generated SBR code, MC code, and MPS code (step S 811 ). The multiplexing unit  22  outputs the encoded audio signal. Now, the audio encoding device  1  ends the coding processing. In step S 811 , the multiplexing unit  22  may multiplex selection information indicating which output the selection unit  16  selects, the first output or the second output. 
     The audio encoding device  1  may execute processing of step S 809  and processing of step S 810  in parallel. Alternatively, the audio encoding device  1  may execute processing of step S 810  before executing processing of step S 809 . 
       FIG. 9A  is a spectrum diagram of an original sound of a multi-channel audio signal.  FIG. 9B  is a spectrum diagram of an audio signal decoded by applying a coding of Embodiment 1. In spectrum diagrams of  FIGS. 9A and 9B , the vertical axis represents the frequency, and the horizontal axis represents the sampling time. As can be understood by comparing  FIGS. 9A and 9B  to each other, reproduction (decoding) of an audio signal approximately similar with a spectrum of the original sound was verified when encoding is performed by applying Embodiment 1. 
       FIG. 10  is a diagram illustrating the coding efficiency when an audio coding according to Embodiment 1 is applied. In  FIG. 10 , sound sources No.  1  and No.  2  are sound sources respectively extracted from different movies. In  FIG. 10 , sound sources No.  1  and No.  2  are sound sources extracted from movies respectively. Sound sources No.  3  and No.  4  are sound sources respectively extracted from different music. All of the sound sources are MPEG surround of 5.1 channels with the sample frequency of 48 kHz and the time length of 60 sec. A first output ratio is a percentage of time of the first output divided by time of the second output. The reduction encoding amount is a reduction amount relative to an encoding amount when encoding is performed by selecting all of second outputs. Reduction of the encoding amount was verified in all of the sound sources. In sound sources No.  1  to No.  4 , a mean value of the first output ratio was 51.3%, and a mean value of the reduction encoding amount was 23.3%. As described above, the audio encoding device according to Embodiment 1 is capable of improving the coding efficiency without degrading the sound quality. 
     (Embodiment 2) 
       FIG. 11  is a functional block diagram of an audio decoding device  100  according to one embodiment. As illustrated in  FIG. 11 , the audio decoding device  100  includes a separation unit  101 , a channel signal decoding unit  102 , a spatial information decoding unit  106 , a restoration unit  107 , a predictive decoding unit  108 , an upmix unit  109 , and a frequency-time transformation unit  110 . The channel signal decoding unit  102  includes an MC decoding unit  103 , a time-frequency transformation unit  104 , and a SBR decoding unit  105 . 
     Those components included in the audio decoding device  100  are formed, for example, as separate hardware circuits by wired logic. Alternatively, those components included in the audio decoding device  100  may be implemented into the audio decoding device  100  as one integrated circuit in which circuits corresponding to respective components are integrated. The integrated circuit may be an integrated circuit such as, for example, an application specific integrated circuit (ASIC) and a field programmable gate array (FPGA). Further, those components included in the audio decoding device  100  may be function modules which are achieved by a computer program implemented on a processor of the audio decoding device  100 . 
     The separation unit  101  receives a multiplexed encoded audio signal from the outside. The separation unit  101  separates an encoded MC code contained in the encoded audio signal, the SBR code, the MPS code, and selection information. The MC code and the SBR code may be referred to as a channel coding code, and the MPS code may be referred to as an encoded spatial information. A separation method described in ISO/IEC14496-3 is available, for example. The separation unit  101  separates the separated MPS code to the spatial information decoding unit  106 , the MC code to the MC decoding unit  103 , the SBR code to the SBR decoding unit  105 , and the selection information to the restoration unit  107 . 
     The spatial information decoding unit  106  receives the MPS code from the separation unit  101 . The spatial information decoding unit  106  decodes the similarity ICC i (k) from the MPS code by using an example of the quantization table relative to the similarity illustrated in  FIG. 4 , and outputs the decoded similarity to the upmix unit  109 . The spatial information decoding unit  106  decodes the intensity difference CLD j (k) from the MPS code by using an example of the quantization table relative to the intensity difference illustrated in  FIG. 6 , and outputs the decoded intensity difference to the upmix unit  109 . The spatial information decoding unit  106  decodes the predictive coefficient from the MPS code by using an example of the quantization table relative to the predictive coefficient illustrated in  FIG. 2 , and outputs the decoded predictive coefficient to the predictive decoding unit  108 . Also, the spatial information decoding unit  106  decodes the amplitude ratio p from the MPS code, and outputs to the restoration unit  107 . 
     The MC decoding unit  103  receives the MC code from the separation unit  101 , decodes a low-region component of channel signals according to the MC decoding method, and outputs to the time-frequency transformation unit  104 . The MC decoding method may be, for example, a method described in ISO/IEC13818-7. 
     The time-frequency transformation unit  104  transforms signals of the respective channels being time signals decoded by the MC decoding unit  103  to frequency signals by using, for example, a QMF filter bank described in ISO/IEC14496-3, and outputs to the SBR decoding unit  105 . The time-frequency transformation unit  104  may perform time-frequency transformation by using a complex QMF filter bank illustrated in the below expression. 
     
       
         
           
             
               
                 
                   
                     
                       QMF 
                       ⁡ 
                       
                         ( 
                         
                           k 
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                     = 
                     
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                       ⁡ 
                       
                         ( 
                         
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                   ⁢ 
                   
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                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
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     Here, QMF(k,n) is a complex QMF using the time “n” and the frequency “k” as variables. 
     The SBR decoding unit  105  decodes a high-region component of channel signals according to the SBR decoding method. The SBR decoding method may be, for example, a method described in ISO/IEC 14496-3. 
     The channel signal decoding unit  102  outputs the stereo frequency signal or the frequency signal of the respective channels decoded by the MC decoding unit  103  and the SBR decoding unit  105  to the restoration unit  107 . 
     The restoration unit  107  receives the amplitude ratio p from the spatial information decoding unit  106 . The restoration unit  107  also receives a frequency signal(s) (a frequency signal of either one of the left frequency signal L 0 (k,n) as an example of the first channel signal and the right frequency signal R 0 (k,n) as an example of the second channel signal, or a stereo frequency signal of both of the left and right frequency signals) from the channel signal decoding unit  102 . Further, the restoration unit  107  also receives, from the separation unit  101 , the selection information indicating an output selected by the selection unit  16 , that is either the first output (either one of the first channel signal and the second channel signal) or the second output (both of the first channel signal and the second channel signal). The restoration unit  107  may not receive the selection information. For example, the restoration unit  107  is also capable of determining based on the number of frequency signals received from the spatial information decoding unit  106  which output the selection unit  16  selects, the first output or the second output. 
     When the selection unit  16  selects the second output, the restoration unit  107  outputs the left frequency signal L 0 (k,n) as an example of the first channel signal and the right frequency signal R 0 (k,n) as an example of the second channel signal to the predictive decoding unit  108 . In other words, the restoration unit  107  outputs the stereo frequency signal to the predictive decoding unit  108 . When the selection unit  16  selects the second output and the restoration unit  107  has received, for example, the left frequency signal L 0 (k,n) as an example of the first channel signal, the restoration unit  107  restores the right frequency signal R 0 (k,n) by integrating the amplitude ratio p to the left frequency signal L 0 (k,n). Also, for example, when the right frequency signal R 0 (k,n) as an example of the second channel signal has been received, the restoration unit  107  restores the left frequency signal L 0 (k,n) by integrating the amplitude ratio p to the right frequency signal R 0 (k,n). Through such restoration processing, the restoration unit  107  outputs the left frequency signal L 0 (k,n) as an example of the first channel signal and the right frequency signal R 0 (k,n) as an example of the second channel signal to the predictive decoding unit  108 . In other words, the restoration unit  107  outputs the stereo frequency signal to the predictive decoding unit  108 . 
     The predictive decoding unit  108  performs predictive decoding of the center-channel signal C 0 (k,n) predictively encoded from a predictive coefficient received from the spatial information decoding unit  106  and a stereo frequency signal received from the restoration unit  107 . For example, the predictive decoding unit  108  is capable of predictively decoding the center-channel signal C 0 (k,n) from a stereo frequency signal and predictive coefficients c 1 (k) and c 2 (k) of the left frequency signal L 0 (k,n) and right frequency signal R 0 (k,n) according to the following equation.
 
 C   0 ( k,n )= c   1 ( k )· L   0 ( k,n )+ c   2 ( k )· R   0 ( k,n )  (Equation 15)
 
     The predictive decoding unit  108  outputs the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the central frequency signal C 0 (k,n) to the upmix unit  109 . 
     The upmix unit  109  performs matrix transformation according to the following equation for the left frequency signal L 0 (k,n), the right frequency signal R 0 (k,n), and the central frequency signal C 0 (k,n), received from the predictive decoding unit  108 . 
     
       
         
           
             
               
                 
                   
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     Here, L OUT (k,n), R OUT (k,n)′ and C OUT (k,n) are respectively left-channel frequency signal, right-channel frequency, and center-channel frequency. The upmix unit  109  upmixes, for example, to a 5.1 channel audio signal, the matrix-transformed left-channel frequency signal L OUT (k,n), right-channel frequency signal R OUT (k,n), center-channel frequency signal C OUT (k,n), and spatial information received from the spatial information decoding unit  106 . Upmixing may be performed by using, for example, a method described in ISO/IEC23003-1. 
     The frequency-time transformation unit  110  performs frequency-to-time transformation of signals received from the upmix unit  109  by using a QMF filter bank indicated in the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       IQMF 
                       ⁡ 
                       
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                     ⁢ 
                     
                         
                     
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     In such a manner, the audio decoding device disclosed in Embodiment 2 is capable of accurately decoding a predictively encoded audio signal with the coding efficiency improved without degrading the sound quality. 
     (Embodiment 3) 
       FIG. 12  is a functional block diagram (Part  1 ) of an audio encoding/decoding system  1000  according to one embodiment.  FIG. 13  is a functional block diagram (Part  2 ) of an audio encoding/decoding system  1000  according to one embodiment. As illustrated in  FIGS. 12 and 13 , the audio encoding/decoding system  1000  includes a time-frequency transformation unit  11 , a first downmix unit  12 , a predictive encoding unit  13 , a second downmix unit  14 , a calculation unit  15 , a selection unit  16 , a channel signal encoding unit  17 , a spatial information encoding unit  21 , and a multiplexing unit  22 . Further, the channel signal encoding unit  17  includes a SBR (Spectral Brand Replication) encoding unit  18 , a frequency-time transformation unit  19 , and an MC (Advanced Audio Coding) encoding unit  20 . Also, the audio encoding/decoding system  1000  includes a separation unit  101 , a channel signal decoding unit  102 , a spatial information decoding unit  106 , a restoration unit  107 , a predictive decoding unit  108 , an upmix unit  109 , and a frequency-time transformation unit  110 . The channel signal decoding unit  102  includes an MC decoding unit  103 , a time-frequency transformation unit  104 , and a SBR decoding unit  105 . Detailed description of functions of the audio encoding/decoding system  1000  is omitted since the functions are same as those illustrated in  FIGS. 1 and 11 . 
     (Embodiment 4) 
     The multi-channel audio signal is digitized with very high sound quality unlike an analog method. On the other hand, such digitized data is characterized in that the data can be easily replicated in a complete format. Accordingly, additional information of copyright information may be embedded in a multi-channel audio signal in a format not perceivable by the user. For example, in the audio encoding device  1  according to Embodiment 1 illustrated in  FIG. 1 , when the selection unit  16  selects the first output, the amount of encoding of either the first channel signal or the second channel signal can be reduced. By allocating a reduced amount of encoding to embedding of additional information, the embedded amount of additional information can be increased up to approximately 2,000 times the second output. The additional information may be stored, for example, in selection information of the FILL element  720  illustrated in  FIG. 7 . The multiplexing unit  22  illustrated in  FIG. 1  may be provided with flag information indicating that additional information is added to selection information. Further, in the audio decoding device  100  according to Embodiment 2, the restoration unit  107  illustrated in  FIG. 11  may detect addition of the additional information based on flag information and extract the additional information stored in the selection information. 
     (Embodiment 5) 
       FIG. 14  is a hardware configuration diagram of a computer functioning as the audio encoding device  1  or the audio decoding device  100  or according to one embodiment. As illustrated in  FIG. 14 , the audio encoding device  1  or the audio decoding device  100  includes a computer  1001  and an input/output device (peripheral device) connected to the computer  1001 . 
     The computer  1001  as a whole is controlled by a processor  1010 . The processor  1010  is connected to a random access memory (RAM)  1020  and a plurality of peripheral devices via a bus  1090 . The processor  1010  may be a multi-processor. The processor  1010  is, for example, a CPU, a micro processing unit (MPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or a programmable logic device (PLD). Further, the processor  1010  may be a combination of two or more elements selected from CPU, MPU, DSP, ASIC and PLD. For example, the processor  1010  is capable of performing in functional blocks illustrated in  FIG. 1 , including the time-frequency transformation unit  11 , the first downmix unit  12 , the predictive encoding unit  13 , the second downmix unit  14 , the calculation unit  15 , the selection unit  16 , the channel signal encoding unit  17 , the spatial information encoding unit  21 , the multiplexing unit  22 , the SBR encoding unit  18 , the frequency-time transformation unit  19 , the MC encoding unit  20 , and so on. Further, the processor  1010  is capable of performing in functional blocks illustrated in  FIG. 11 , such as the separation unit  101 , the channel signal decoding unit  102 , the MC decoding unit  103 , the time-frequency transformation unit  104 , the SBR decoding unit  105 , the spatial information decoding unit  106 , the restoration unit  107 , predictive decoding unit  108 , upmix unit  109 , the frequency-time transformation unit  110 , and so on. 
     The RAM  1020  is used as a main storage device of the computer  1001 . The RAM  1020  temporarily stores at least a portion of programs of an operating system (OS) for running the processor  1010  and an application program. Further, the RAM  1020  stores various data to be used for processing by the processor  1010 . 
     Peripheral devices connected to the bus  1090  include a hard disk drive (HDD)  1030 , a graphic processing device  1040 , an input interface  1050 , an optical drive device  1060 , a device connection interface  1070 , and a network interface  1080 . 
     The HDD  1030  magnetically writes and reads data from an integrated disk. For example, the HDD  1030  is used as an auxiliary storage device of the computer  1001 . The HDD  1030  stores an OS program, an application program, and various data. The auxiliary storage device may include a semiconductor memory device such as a flash memory. 
     The graphic processing device  1040  is connected to a monitor  1100 . The graphic processing device  1040  displays various images on a screen of the monitor  1100  in accordance with an instruction given by the processor  1010 . A display device and a liquid crystal display device using cathode ray tube (CRT) are available as the monitor  1100 . 
     The input interface  1050  is connected to a keyboard  1110  and a mouse  1120 . The input interface  1050  transmits signals sent from the keyboard  1110  and the mouse  1120  to the processor  1010 . The mouse  1120  is an example of pointing devices. Thus, another pointing device may be used. Other pointing devices include a touch panel, a tablet, a touch pad, a truck ball, and so on. 
     The optical drive device  1060  reads data stored in an optical disk  1130  by utilizing a laser beam. The optical disk  1130  is a portable recording medium in which data is recorded in a manner allowing readout by light reflection. The optical disk  1130  includes a digital versatile disc (DVD), a DVD-RAM, a Compact Disc Read-Only Memory (CD-ROM), a CD-Recordable (R)/ReWritable (RW), and so on. A program stored in the optical disk  1130  serving as a portable recording medium is installed in the audio encoding device or the audio decoding device  100  via the optical drive device  1060 . A given program installed may be executed on the audio encoding device  1  or the audio decoding device  100 . 
     The device connection interface  1070  is a communication interface for connecting peripheral devices to the computer  1001 . For example, the device connection interface  1070  may be connected to a memory device  1140  and a memory reader writer  1150 . The memory device  1140  is a recording medium having a function for communication with the device connection interface  1070 . The memory reader writer  1150  is a device configured to write data into a memory card  1160  or read data from the memory card  1160 . The memory card  1160  is a card type recording medium. 
     A network interface  1080  is connected to a network  1170 . The network interface  1080  transmits and receives data from other computers or communication devices via the network  1170 . 
     The computer  1001  implements, for example, the above mentioned graphic processing function by executing a program recorded in a computer readable recording medium. A program describing details of processing to be executed by the computer  1001  may be stored in various recording media. The above program may comprise one or more function modules. For example, the program may comprise function modules which implement processing illustrated in  FIG. 1 , such as the time-frequency transformation unit  11 , the first downmix unit  12 , the predictive encoding unit  13 , the second downmix unit  14 , the calculation unit  15 , the selection unit  16 , the channel signal encoding unit  17 , the spatial information encoding unit  21 , the multiplexing unit  22 , the SBR encoding unit  18 , the frequency-time transformation unit  19 , and the MC encoding unit  20 . Further, the program may comprise function modules which implement processing illustrated in  FIG. 11 , such as the separation unit  101 , the channel signal decoding unit  102 , the AAC decoding unit  103 , the time-frequency transformation unit  104 , the SBR decoding unit  105 , the spatial information decoding unit  106 , the restoration unit  107 , predictive decoding unit  108 , the upmix unit  109 , and the frequency-time transformation unit  110 . A program to be executed by the computer  1001  may be stored in the HDD  1030 . The processor  1010  implements a program by loading at least a portion of a program stored in the HDD  1030  into the RAM  1020 . A program to be executed by the computer  1001  may be stored in a portable recording medium such as the optical disk  1130 , the memory device  1140 , and the memory card  1160 . A program stored in a portable recording medium becomes ready to run, for example, after being installed on the HDD  1030  by control through the processor  1010 . Alternatively, the processor  1010  may run the program by directly reading from a portable recording medium. 
     In Embodiments described above, components of illustrated respective devices may not be physically configured as illustrated. That is, specific separation and integration of devices are not limited to those illustrated, and devices may be configured by separating and/or integrating a whole or a portion thereof on any basis depending on various loads and utilization status. 
     Further, according to other embodiments, channel signal coding of the audio encoding device may be performed by encoding the stereo frequency signal according to a different coding method. For example, the channel signal encoding unit may encode all of frequency signals in accordance with the MC coding method. In this case, the SBR encoding unit in the audio encoding device illustrated in  FIG. 1  is omitted. 
     Multi-channel audio signals to be encoded or decoded are not limited to the 5.1 channel signal. For example, audio signals to be encoded or decoded may be audio signals having a plurality of channels such as 3 channels, 3.1 channels or 7.1 channels. In this case, the audio encoding device also calculates frequency signals of the respective channels by performing time-frequency transformation of audio signals of the channels. Then, the audio encoding device downmixes frequency signals of the channels to generate a frequency signal with the number of channels less than an original audio signal. 
     Audio coding devices according to the above embodiments may be implemented on various devices utilized for conveying or recording an audio signal, such as a computer, a video signal recorder or a video transmission apparatus. 
     All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.