Abstract:
An audio signal decoding apparatus is provided that includes a receiver that receives an encoded information, a memory, and a processor that demultiplexes low-band encoding parameters, index information, and scale factor information from the encoded information. The processor also decodes the low-band encoding parameters to obtain a synthesized low frequency spectrum, replicates a high frequency subband spectrum based on the index information using the synthesized low frequency spectrum, and adjusts an amplitude of the replicated high frequency subband spectrum using the scale factor information. The processor further estimates a frequency of a harmonic component in the synthesized low frequency spectrum, adjusts a frequency of a harmonic component in the high frequency subband spectrum using the estimated harmonic frequency spectrum, and generates an output signal using the synthesized low frequency spectrum and the high frequency subband spectrum.

Description:
This is a continuation application of pending U.S. patent application Ser. No. 14/894,062, filed Nov. 25, 2015, which is a U.S. National Stage of International Application No. PCT/JP2014/003103 filed Jun. 10, 2014, which claims the benefit of Japanese Application No. 2013-122985, filed Jun. 11, 2013, the contents of all of which are expressly incorporation by reference herein in their entireties. 
    
    
     TECHNICAL FIELD 
     The present invention relates to audio signal processing, and particularly to audio signal encoding and decoding processing for audio signal bandwidth extension. 
     BACKGROUND ART 
     In communications, to utilize the network resources more efficiently, audio codecs are adopted to compress audio signals at low bitrates with an acceptable range of subjective quality. Accordingly, there is a need to increase the compression efficiency to overcome the bitrate constraints when encoding an audio signal. 
     Bandwidth extension (BWE) is a widely used technique in encoding an audio signal to efficiently compress wideband (WB) or super-wideband (SWB) audio signals at a low bitrate. In encoding, BWE parametrically represents a high frequency band signal utilizing the decoded low frequency band signal. That is, BWE searches for and identifies a portion similar to a subband of the high frequency band signal from the low frequency band signal of the audio signal, and encodes parameters which identify the similar portion and transmit the parameters, while BWE enables high frequency band signal to be resynthesized utilizing the low frequency band signal at a signal-receiving side. It is possible to reduce the amount of parameter information to be transmitted, by utilizing a similar portion of the low frequency band signal, instead of directly encoding the high frequency band signal, thus increasing the compression efficiency. 
     One of the audio/speech codecs which utilize BWE functionality is G.718-SWB, whose target applications are VoIP devices, video-conference equipments, tele-conference equipments and mobile phones. 
     The configuration of G.71.8-SWB [1] is illustrated in  FIGS. 1 and 2  (see, e.g., Non-Patent Literature (hereinafter, referred to as “NPL”) 1). 
     At an encoding apparatus side illustrated in  FIG. 1 , the audio signal (hereinafter, referred to as input signal) sampled at 32 kHz is firstly down-sampled to 16 kHz ( 101 ). The down-sampled signal is encoded by the G.718 core encoding section ( 102 ). The SWB bandwidth extension is performed in MDCT domain. The 32 kHz input signal is transformed to MDCT domain ( 103 ) and processed through a tonality estimation section ( 104 ). Based on the estimated tonality of the input signal ( 105 ), generic mode ( 106 ) or sinusoidal mode ( 108 ) is used for encoding the first layer of SWB. Higher SWB layers are encoded using additional sinusoids ( 107  and  109 ). 
     The generic mode is used when the input frame signal is not considered to be tonal. In the generic mode, the MDCT coefficients (spectrum) of the WB signal encoded by a G.718 core encoding section are utilized to encode the SWB MDCT coefficients (spectrum). The SWB frequency band (7 to 14 kHz) is split into several subbands, and the most correlated portion is searched for every subband from the encoded and normalized WB MDCT coefficients. Then, a gain of the most correlated portion is calculated in terms of scale such that the amplitude level of SWB subband is reproduced to obtain parametric representation of the high frequency component of SWB signal. 
     The sinusoidal mode encoding is used in frames that are classified as tonal. In the sinusoidal mode, the SWB signal is generated by adding a finite set of sinusoidal components to the SWB spectrum. 
     At a decoding apparatus side illustrated in  FIG. 2 , the G.718 core codec decodes the WB signal at 16 kHz sampling rate ( 201 ). The WB signal is post-processed ( 202 ), and then up-sampled ( 203 ) to 32 kHz sampling rate. The SWB frequency components are reconstructed by SWB bandwidth extension. The SWB bandwidth extension is mainly performed in MDCT domain. Generic mode ( 204 ) and sinusoidal mode ( 205 ) are used for decoding the first :layer of the SWB. Higher SWB layers are decoded using an additional sinusoidal mode ( 206  and  207 ). The reconstructed SWB MDCT coefficients are transformed to a time domain ( 208 ) followed by post-processing ( 209 ), and then added to the WB signal decoded by the G.718 core decoding section to reconstruct the SWB output signal in the time domain, 
     CITATION LIST 
     Non-Patent Literature 
     NPL 1: ITU-T Recommendation G.718 Amendment 2, New Annex B on super wideband scalable extension for ITU-T G.718 and corrections to main body fixed-point C-code and description text, March 2010. 
     SUMMARY OF INVENTION 
     Technical Problem 
     As it can be seen in G.718-SWB configuration, the input signal SWB bandwidth extension is performed by either sinusoidal mode or generic mode. 
     For generic encoding mechanism, for example, high frequency components are generated (obtained) by searching for the most correlated portion from the WB spectrum. This type of approach usually suffers from performance problems especially for signals with harmonics. This approach doesn&#39;t maintain the harmonic relationship between the low frequency band harmonic components (tonal components) and the replicated high frequency band tonal components at all, which becomes the cause of ambiguous spectra that degrade the auditory quality, 
     Therefore, in order to suppress the perceived noise (or artifacts), which is generated due to ambiguous spectra or due to disturbance in the replicated high frequency band signal spectrum (high frequency spectrum), it is desirable to maintain the harmonic relationship between the low frequency band signal spectrum (low frequency spectrum) and the high frequency spectrum. 
     In order to solve this problem, G.718-SWB configuration is equipped with the sinusoidal mode. The sinusoidal mode encodes important tonal components using a sinusoidal wave, and thus it can maintain the harmonic structure well. However, the resultant sound quality is not good enough only by simply encoding the SWB component with artificial tonal signals. 
     Solution to Problem 
     An object of the present invention is to improve the performance of encoding a signal with harmonics, which causes the performance problems in the above-described generic mode, and to provide an efficient method for maintaining the harmonic structure of is the tonal component between the low frequency spectrum and the replicated high frequency spectrum, maintaining the fine structure of the spectra. Firstly, a relationship between the low frequency spectrum tonal component and the high frequency spectrum tonal component is obtained by estimating a harmonic frequency value from the WB spectrum. Then, the low frequency spectrum encoded at the encoding apparatus side is decoded, and, according to index information, a portion which is the most correlated with a subband of the high frequency spectrum is copied into the high frequency band with being adjusted in energy levels, thereby replicating the high frequency spectrum. The frequency of the tonal component in the replicated high frequency spectrum is identified or adjusted based on an estimated harmonic frequency value. 
     The harmonic relationship between the low frequency spectrum tonal components and the replicated high frequency spectrum tonal components can be maintained only when the estimation of a harmonic frequency is accurate. Therefore, in order to improve the accuracy of the estimation, the correction of spectral peaks constituting the tonal components is performed before estimating the harmonic frequency. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to accurately replicate the tonal component in the high frequency spectrum reconstructed by bandwidth extension for an input signal with harmonic structure, and to efficiently obtain good sound quality at low bitrate. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  illustrates the configuration of a G.718-SWB encoding apparatus; 
         FIG. 2  illustrates the configuration of a G.718-SWB decoding apparatus; 
         FIG. 3  is a block diagram illustrating the configuration of an encoding apparatus according to Embodiment 1 of the present invention; 
         FIG. 4  is a Hock diagram illustrating the configuration of a decoding apparatus according to Embodiment 1 of the present invention; 
         FIG. 5  is a diagram illustrating an approach for correcting the spectral peak detection; 
         FIG. 6  is a diagram illustrating an example of a harmonic frequency adjustment method; 
         FIG. 7  is a diagram illustrating another example of a harmonic frequency adjustment method; 
         FIG. 8  is a block diagram illustrating the configuration of an encoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 9  is a block diagram illustrating the configuration of a decoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 10  is a block diagram illustrating the configuration of an encoding apparatus according to Embodiment 3 of the present invention; 
         FIG. 11  is a block diagram illustrating the configuration of a decoding apparatus according to Embodiment 3 of the present invention; 
         FIG. 12  is a block diagram illustrating the configuration of a decoding apparatus according to Embodiment 4 of the present invention; 
         FIG. 13  is a diagram illustrating an example of a harmonic frequency adjustment method for a synthesized low frequency spectrum; and 
         FIG. 14  is a diagram illustrating an example of an approach for injecting missing harmonics into the synthesized low frequency spectrum. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The main principle of the present invention is described in this section using  FIGS. 3 to 14 . Those skilled in the art will be able to modify or adapt the present invention without deviating from the spirit of the invention. 
     (Embodiment 1) 
     The configuration of a codec according to the present invention is illustrated in  FIGS. 3 and 4 . 
     At an encoding apparatus side illustrated in  FIG. 3 , a sampled input signal is firstly down-sampled ( 301 ). The down-sampled low frequency band signal (low frequency signal) is encoded by a core encoding section ( 302 ). Core encoding parameters are sent to a multiplexer ( 307 ) to form a bitstream. The input signal is transformed to a frequency domain signal using a time-frequency (RE) transformation section ( 303 ), and its high frequency band signal (high frequency signal) is split into a plurality of subbands. The encoding section may be an existing narrow band or wide band audio of speech codec, and one example is G.718. The core encoding section ( 302 ) not only performs encoding but also has a local decoding section and a time-frequency transformation section to perform local decoding and time-frequency transformation of the decoded signal (synthesized signal) to supply the synthesized low frequency signal to an energy normalization section ( 304 ). The synthesized low frequency signal of the normalized frequency domain is utilized for the bandwidth extension as follows. Firstly, a similarity search section ( 305 ) identifies a portion which is the most correlated with each subband of the high frequency signal of the input signal, using the normalized synthesized low frequency signal, and sends the index information as search results to a multiplexing section ( 307 ). Next, the information of scale factors between the most correlated portion and each subband of the high frequency signal of the input signal is estimated ( 306 ), and encoded scale factor information is sent to the multiplexing section ( 307 ). 
     Finally, the multiplexing section ( 307 ) integrates the core encoding parameters, the index information and the scale factor information into a bitstream. 
     In a decoding apparatus illustrated in  FIG. 4 , a demultiplexing section ( 401 ) unpacks the bitstream to obtain the core encoding parameters, the index information and the scale factor information. 
     A core decoding section reconstructs synthesized low frequency signals using the core encoding parameters ( 402 ). The synthesized low frequency signal is up-sampled ( 403 ), and used for bandwidth extension ( 410 ). 
     This bandwidth extension is performed as follows. That is, the synthesized low frequency signal is energy-normalized ( 404 ), and a low frequency signal identified according to the index information that identifies a portion which is the most correlated with each subband of the high frequency signal of the input signal derived at the encoding apparatus side is copied into the high frequency band ( 405 ), and the energy level is adjusted according to the scale factor information to achieve the same level of the energy level of the high frequency signal of the input signal ( 406 ). 
     Further, a harmonic frequency is estimated from the synthesized low frequency spectrum ( 407 ). The estimated harmonic frequency is used to adjust the frequency of the tonal component in the high frequency signal spectrum ( 408 ). 
     The reconstructed high frequency signal is transformed from a frequency domain to a time domain ( 409 ), and is added to the up-sampled synthesized low frequency signal to generate an output signal in the time domain. 
     The detail processing of a harmonic frequency estimation scheme will be described as follows:
     1) From the synthesized low frequency signal (LF) spectrum, a portion for estimating a harmonic frequency is selected. The selected portion should have clear harmonic structure so that the harmonic frequency estimated from the selected portion is reliable. Usually, for every harmonic, a clear harmonic structure is observed from 1 to 2 kHz to around a cut-off frequency.   2) The selected portion is split into a multiplicity of blocks with a width near to a human&#39;s voice pitch frequency (about 100 to 400 Hz).   3) Spectral peaks, which are the spectrum whose amplitude is the maximum within each block, and spectral peak frequencies, which are the frequencies of those spectral peaks, are searched.   4) Post-processing is performed to the identified spectral peaks in order to avoid errors or to improve the accuracy in the harmonic frequency estimation,   

     The spectrum illustrated in  FIG. 5  is used to describe an example of the post-processing. 
     Based on the synthesized low frequency signal spectrum, spectral peaks and spectral peak frequencies are calculated. However, a spectral peak with a small amplitude and extremely short spacing of a spectral peak frequency with respect to an adjacent spectral peak is discarded, which avoids estimation errors in calculating a harmonic frequency value.
     1) The spacing between the identified spectral peak frequencies is calculated.   2) A harmonic frequency is estimated based on the spacing between the identified spectral peak frequencies. One of the methods for estimating the harmonic frequency is presented as follows:   

     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           Spacing 
                           peak 
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       = 
                       
                         
                           
                             Pos 
                             peak 
                           
                           ⁡ 
                           
                             ( 
                             
                               n 
                               + 
                               1 
                             
                             ) 
                           
                         
                         - 
                         
                           
                             Pos 
                             peak 
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       n 
                       ∈ 
                       
                         [ 
                         
                           1 
                           , 
                           
                             N 
                             - 
                             1 
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       Est 
                       Harmonic 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             1 
                           
                           
                             N 
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             Spacing 
                             peak 
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                       
                         N 
                         - 
                         1 
                       
                     
                   
                 
               
               
                 
                   [ 
                   1 
                   ] 
                 
               
             
           
         
       
     
     where 
     Est Harmonic  is the calculated harmonic frequency; 
     Spacing peak  is the frequency spacing between the detected peak positions; 
     N is the number of the detected peak positions; 
     Pos peak  is the position of the detected peak; 
     The harmonic frequency estimation is also performed according to a method described as follows:
     1) In the synthesized low frequency signal (LF) spectrum, in order to estimate a harmonic frequency, a portion having a clear harmonic structure is selected so that the estimated harmonic frequency is reliable. Usually, for every harmonic, a clear harmonic structure can be seen from 1 to 2 kHz to around a cut-off frequency.   2) A spectrum and its frequency having the maximum amplitude (absolute value) are identified within the selected portion of the above-mentioned synthesized low frequency signal (spectrum).   3) A set of spectral peaks having a substantially equal frequency spacing from the spectrum frequency of the spectrum with the maximum amplitude and at which the absolute value of the amplitude exceeds a predetermined threshold is identified. As the predetermined threshold, it is possible to apply, for example, a value twice the standard deviation of the spectral amplitudes contained in the above-mentioned selected portion.   4) The spacing between the above-mentioned spectral peak frequencies is calculated.   5) The harmonic frequency is estimated based on the spacing between the above-mentioned spectral peak frequencies. Also in this case, the method in Equation (1) can be used to estimate the harmonic frequency.   

     There is a case where the harmonic component in the synthesized low frequency signal spectrum is not well encoded, at a very low bitrate. In this case, there is a possibility that some of the spectral peaks identified may not correspond to the harmonic components of the input signals at all. Therefore, in the calculation of the harmonic frequency, the spacing between spectral peak frequencies which are largely different from the average value should be excluded from the calculation target. 
     Also, there is a case where not all the harmonic components can be encoded (meaning that some of the harmonic components are missing in the synthesized low frequency signal spectrum) due to the relatively low amplitude of the spectral peak, the bitrate constraints for encoding, or the like. In these cases, the spacing between the spectral peak frequencies extracted at the missing harmonic portion is considered to be twice or a few times the spacing between the spectral peak frequencies extracted at the portion which retains good harmonic structure. In this case, the average value of the extracted values of the spacing between the spectral peak frequencies where the values are included in the predetermined range including the maximum spacing between the spectral peak frequencies is defined as an estimated harmonic frequency value. Thus, it becomes possible to properly replicate the high frequency spectrum. The specific procedure comprises the following steps:
     1) The minimum and maximum values of the spacing between the spectral peak frequencies are identified;   

     [2]
 
Spacing peak ( n )=Pos peak ( n+ 1)−Pos peak ( n ),  nε[ 1, N− 1]
 
Spacing mix =min({Spacing peak ( n )});
 
Spacing max =max({Spacing peak ( n )});  (Equation 2)
 
     where; 
     Spacing peak  is the frequency spacing between the detected peak positions; 
     Spacing min  is the minimum frequency spacing between the detected peak positions; 
     Spacing max  is the maximum frequency spacing between the detected peak positions; 
     N is the number of the detected peak positions; 
     Pos peak  is the position of the detected peak; 
     2) Every spacing between spectral peak frequencies is identified in the range of: 
     [3]
 
[ k *Spacing min ,Spacing max ],  k ε[1,2]
 
     3) The average value of the identified spacing values between the spectral peak frequencies in the above range is defined as the estimated harmonic frequency value. 
     Next, one example of harmonic frequency adjustment schemes will be described below, 
     1) The last encoded spectral peak and its spectral peak frequency are identified in to the synthesized low frequency signal (LF) spectrum. 
     2) The spectral peak and the spectral peak frequency are identified within the high frequency spectrum replicated by bandwidth extension. 
     3) Using the highest spectral peak frequency as a reference, among spectral peaks of the synthesized low frequency signal spectrum, the spectral peak frequencies are adjusted so that the values of the spacing between the spectral peak frequencies are equal to the estimated value of the spacing between the harmonic frequencies. This processing is illustrated in  FIG. 6 . As illustrated in  FIG. 6 , firstly, the highest spectral peak frequency in the synthesized low frequency signal spectrum and the spectral peaks in the replicated high frequency spectrum are identified. Then, the lowest spectral peak frequency in the replicated high frequency spectrum is shifted to the frequency having a spacing of Est Harmonic  from the highest spectral peak frequency of the synthesized low frequency signal spectrum. The second lowest spectral peak frequency in the replicated high frequency spectrum is shifted to the frequency having a spacing of Est Harmonic  from the above-mentioned, shifted lowest spectral peak frequency. The processing is repeated until such an adjustment is completed for every spectral peak frequency of the spectral peak in the replicated high frequency spectrum. 
     Harmonic frequency adjustment schemes as described below are also possible.
     1) The synthesized low frequency signal (LF) spectrum having the highest spectral peak frequency is identified.   2) The spectral peak and the spectral peak frequency within the high frequency (HF) spectrum extended in terms of bandwidth by bandwidth extension are identified.   3) Using the highest spectral peak frequency of the synthesized low frequency signal spectrum as a reference, possible spectral peak frequencies in the HR spectrum are calculated. Each spectral peak in the high frequency spectrum replicated by the bandwidth extension is shifted to a frequency which is the closest to each spectral peak frequency, among the calculated spectral peak frequencies. This processing is illustrated in  FIG. 7 . As illustrated in  FIG. 7 , firstly, the synthesized low frequency spectrum having the highest spectral peak frequency and the spectral peaks in the replicated high frequency spectrum are extracted. Then, possible spectral peak frequency in the replicated high frequency spectrum is calculated. The frequency having a spacing of Est Harmonic  from the highest spectral peak frequency of the synthesized low frequency signal spectrum is defined as a spectral peak frequency which may be the first spectral peak frequency in the replicated high frequency spectrum. Next, the frequency having a spacing of Est Harmonic  from the above-mentioned spectral peak frequency which may be the first spectral peak frequency is defined as a spectral peak frequency which may be the second spectral peak frequency. The processing is repeated as long as the calculation is possible in the high frequency spectrum.   

     Thereafter, the spectral peak extracted in the replicated high frequency spectrum is shifted to a frequency which is the closest to the spectral peak frequency, among the possible spectral peak frequencies calculated as described above. 
     There is also a case where the estimated harmonic value Est Harmonic  does not correspond to an integer frequency bin. In this case, the spectral peak frequency is selected to be a frequency bin which is the closest to the frequency derived based on Est Harmonic . 
     There also may be a method of estimating a harmonic frequency in which the previous frame spectrum is utilized to estimate the harmonic frequency, and a method of adjusting the frequencis of tonal components in which the previous frame spectrum is taken into consideration so that the transition between frames is smooth when adjusting the tonal component. It is also possible to adjust the amplitude such that, even when the frequencies of the tonal components are shifted, the energy level of the original spectrum is maintained. All such minor variations are within the scope of the present invention. 
     The above descriptions are all given as examples, and the ideas of the present invention are not limited by the given examples. Those skilled in the art will be able to modify and adapt the present invention without deviating from the spirit of the invention. 
     [Effect] 
     The bandwidth extension method according to the present invention replicates the high frequency spectrum utilizing the synthesized low frequency signal spectrum which is the most correlated with the high frequency spectrum, and shifts the spectral peaks to the estimated harmonic frequencies. Thus, it becomes possible to maintain both the fine structure of the spectrum and the harmonic structure between the low frequency band spectral peaks and the replicated high frequency band spectral peaks. 
     (Embodiment 2) 
     Embodiment 2 of the present invention is illustrated in  FIGS. 8 and 9 . 
     The encoding apparatus according to Embodiment 2 is substantially the same as that of Embodiment 1, except harmonic frequency estimation sections ( 708  and  709 ) and a harmonic frequency comparison section ( 710 ). 
     The harmonic frequency is estimated separately from synthesized low frequency spectrum ( 708 ) and high frequency spectrum ( 709 ) of the input signal, and flag information is transmitted based on the comparison result between the estimated values of those ( 710 ). As one of the examples, the flag information can be derived as in the following equation: 
     [4] 
     if
 
Est Harmonic   _   LF ε[Est Harmonic   _   HF −Threshold, Est Harmonic   _   HF +Threshold]
 
Flag=1
 
Otherwise
 
Flag=0  (Equation 3)
 
where
     Est Harmonic   _   LF  is the estimated harmonic frequency from the synthesized low frequency spectrum;   Est Harmonic   _   HF  is the estimated harmonic frequency from the original high frequency spectrum;   Threshold is a predetermined threshold for the difference between Est Harmonic   _   LF  and Est Harmonic    _   HF ;   Flag is the flag signal to indicate whether the harmonic adjustment should be applied;   

     That is, the harmonic frequency estimated from the synthesized low frequency signal spectrum (synthesized low frequency spectrum) Est Harmonic   _   LF  is compared with the harmonic frequency estimated from the high frequency spectrum of the input signal Est Harmonic   _   HF . When the difference between the two values is small enough, it is considered that the estimation from the synthesized low frequency spectrum is accurate enough, and a flag (Flag=1) meaning that it may be used for harmonic frequency adjustment is set. On the other hand, when the difference between the two values is not small, it is considered that the estimated value from the synthesized low frequency spectrum is not accurate, and a flag (Flag=0) meaning that it should not be used for harmonic frequency adjustment is set. 
     At decoding apparatus side illustrated in  FIG. 9 , the value of the flag information determines whether or not the harmonic frequency adjustment ( 810 ) is applied to the replicated high frequency spectrum. That is, in the case of Flag=1, the decoding apparatus performs harmonic frequency adjustment, whereas in the case of Flag=0, it does not perform harmonic frequency adjustment. 
     [Effect] 
     For several input signals, there is a case where the harmonic frequency estimated from the synthesized low frequency spectrum is different from the harmonic frequency of the high frequency spectrum of the input signal. Especially at low bitrate, the harmonic structure of the low frequency spectrum is not well maintained. By sending the flag information, it becomes possible to avoid the adjustment of the tonal component using a wrongly estimated value of the harmonic frequency. 
     (Embodiment 3) 
     Embodiment 3 of the present invention is illustrated in  FIGS. 10 and 11 . 
     The encoding apparatus according to Embodiment 3 is substantially the same as that of Embodiment 2, except differential device ( 910 ). 
     The harmonic frequency is estimated separately from the synthesized low frequency spectrum ( 908 ) and high frequency spectrum ( 909 ) of the input signal. The difference between the two estimated harmonic frequencies (Diff) is calculated ( 910 ), and transmitted to the decoding apparatus side. 
     At decoding apparatus side illustrated in  FIG. 11 , the difference value (Diff) is added to the estimated value of the harmonic frequency from the synthesized low frequency spectrum ( 1010 ), and the newly calculated value of the harmonic frequency is used for the harmonic frequency adjustment in the replicated high frequency spectrum. 
     Instead of the difference value, the harmonic frequency estimated from the high frequency spectrum of the input signal may also be directly transmitted to the decoding section. Then, the received harmonic frequency value of the high frequency spectrum of the input signal is used to perform the harmonic frequency adjustment. Thus, it becomes unnecessary to estimate the harmonic frequency from the synthesized low frequency spectrum at the decoding apparatus side. 
     [Effect] 
     There is a case where, for several signals, the harmonic frequency estimated from the synthesized low frequency spectrum is different from the harmonic frequency of the high frequency spectrum of the input signal. Therefore, by sending the difference value, or the harmonic frequency value derived from the high frequency spectrum of the input signal, it becomes possible to adjust the tonal component of the high frequency spectrum replicated through bandwidth extension by the decoding apparatus at the receiving side more accurately. 
     Embodiment 4) 
     Embodiment 4 of the present invention is illustrated in  FIG. 12 . 
     The encoding apparatus according to Embodiment 4 is the same as any other conventional encoding apparatuses,or is the same as the encoding apparatus in Embodiment 1, 2 or 3. 
     At decoding apparatus side illustrated in  FIG. 12 , the harmonic frequency is estimated from the synthesized low frequency spectrum ( 1103 ). The estimated value of this harmonic frequency is used for harmonic injection ( 1104 ) in the low frequency spectrum. 
     Especially when the available bitrate is low, there is a case where some of the harmonic components of the low frequency spectrum are hardly encoded, or are not encoded at all. In this case, the estimated harmonic frequency value can be used to inject the missing harmonic components. 
     This will be illustrated in the  FIG. 13 . It can be seen, from  FIG. 13 , that there is a missing harmonic component in the synthesized low frequency (LE) spectrum. Its frequency can be derived using the estimated harmonic frequency value. Further, as for its amplitude, for example, it is possible to use the average value of the amplitudes of other existing spectral peaks or the average value of the amplitudes of the existing spectral peaks neighboring to the missing harmonic component on the frequency axis. The harmonic component generated according to the frequency and amplitude is injected for restoring the missing harmonic component. 
     Another approach for injecting the missing harmonic component will be described as follows:
     1. The harmonic frequency is estimated using the encoded LE spectrum ( 1103 ).   1.1 The harmonic frequency is estimated using spacing between spectral peak frequencies identified in the encoded low frequency spectrum.   1.2 The values of spacing between the spectral peak frequencies, which are derived from the missing harmonic portion, become twice or a few times of values of the spacing between the spectral peak frequencies, which are derived from a portion which has a good harmonic structure. Such values of the spacing between the spectral peak frequencies are grouped into different categories, and the average spacing value between the spectral peak frequencies is estimated for each of the categories. The detail thereof will be described as follows:   a. The minimum value and the maximum value of the spacing value between the spectral peak frequencies are identified.   

     [5]
 
Spacing peak ( n )=Pos peak ( n+ 1)−Pos peak ( n ),  n ε[1,  N− 1]
 
Spacing min =min({Spacing peak ( n )});
 
Spacing max =max({Spacing peak ( n )});  (Equation 4)
 
     where; 
     Spacing peak  is the frequency spacing between the detected peak positions; 
     Spacing min  is the minimum frequency spacing between the detected peak positions; 
     Spacing max  is the maximum frequency spacing between the detected peak positions; 
     N is the number of the detected peak positions; 
     Pos peak  is the position of the detected peak;
     b. Every spacing value is identified in the range of:   

     [6]
 
 r   1 =[Spacing min   ,k *Spacing min )
 
 r   2 =[ k *Spacing min , Spacing max ], 1&lt; k≦ 2
     c. The average values of the spacing values identified in the above ranges are calculated as the estimated harmonic frequency values.   

     
       
         
           
             
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         Est 
                         
                           Harmonic 
                           
                             LF 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             
                               Spacing 
                               peak 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         
                           N 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           Spacing 
                           peak 
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ∈ 
                       
                         r 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         Est 
                         
                           Harmonic 
                           
                             LF 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             
                               Spacing 
                               peak 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         
                           N 
                           2 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           Spacing 
                           peak 
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ∈ 
                       
                         r 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   7 
                   ] 
                 
               
             
           
         
       
     
     where 
     Est Harmonic     LF1   , Est Harmonic     LF2    are the estimated harmonic frequencies 
     N 1  is the number of the detected peak positions belonging to r 1    
     N 2  is the number of the detected peak positions belonging to r 2  
     2. Using the estimated harmonic frequency values, the missing harmonic components are injected.   2.1 The selected LF spectrum is split into several regions.   2.2 The missing harmonics are identified by utilizing region information and the estimated frequencies.   

     For example, assume that the selected LF spectrum is split into three regions r 1 , r 2 , and r 3 . 
     Based on the region information, the harmonics are identified and injected. 
     Due to the signal characteristics for harmonics, the spectral gap between harmonics is Est Harmonic     LF1    in r1 and r2 regions, and is Est Harmonic     LF2    in r3 region. This information can be used for extending the LF spectrum. This is illustrated further in  FIG. 14 . It can be seen, from  FIG. 14 , that there is a missing harmonic component in the domain r 2  of the LF spectrum. This frequency can be derived using the estimated harmonic frequency value Est LF1 . 
     Similarly, Est Harmonic     LF2    is used for tracking and injecting the missing harmonic in region r 3 . 
     Further, as for its amplitude, it is possible to use the average value of the amplitudes of all the harmonic components which are not missing or the average value of the amplitudes of the harmonic components preceding and following the missing harmonic component. Alternatively, as for the amplitude, a spectral peak with the minimum amplitude in the WB spectrum may be used. The harmonic component generated using the frequency and amplitude is injected into the LF spectrum for restoring the missing harmonic component. 
     [Effect] 
     There is a case where the synthesized low frequency spectrum is not maintained for several signals. Especially at low bitrate, there is a possibility that several harmonic components may be missing. By injecting the missing harmonic components in the LF spectrum, it becomes possible not only to extend the LF, but also improve the harmonic characteristics of the reconstructed harmonics. This can suppress the auditory influence due to missing harmonics to further improve the sound quality. 
     The disclosure of Japanese Patent Application No. 2013-122985 filed on Jun. 11, 2013, including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
     INDUSTRIAL APPLICABILITY 
     The encoding apparatus, decoding apparatus and encoding and decoding methods according to the present invention are applicable to a wireless communication terminal apparatus, base station apparatus in a mobile communication system, tele-conference terminal apparatus, video conference terminal apparatus, and voice over Internet protocol (VOIP) terminal apparatus.