Patent Publication Number: US-2005143973-A1

Title: Digital signal sub-band separating/combining apparatus achieving band-separation and band-combining filtering processing with reduced amount of group delay

Description:
BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The invention relates to a sub-band separating/combining apparatus having a band-separating filter bank for converting a digital signal to a plurality of sub-band signals and a band-combining filter bank which receives the sub-band signals after processing or transmission thereof, for combining these to recover the original digital signal or a processed version of that signal  
      2. Description of the Related Art  
      There are various applications in which a digital signal is supplied to a set of filters of a band-separating filter bank (sometimes referred to as an analyzing filter bank) to be spectrally divided into a plurality of sub-band signals, i.e., respectively corresponding to different frequency bands, with the sample rate of each of the sub-band signals then being reduced by decimation (i.e., down-sampling). Processing or transmission of the resultant low-bandwidth sub-band signals can then be efficiently performed. After processing or transmission of the sub-band signals, they are supplied to a band-combining filter bank (sometimes referred to as a synthesizing or a reconstructing filter bank), to be each subjected to interpolation processing (i.e., up-sampling), then inputted to respective ones of a set of filters whose outputs are additively combined to recover the original digital signal (or a processed version of that signal).  
      A prior art example of such a combination of a band-separating filter bank and a band-combining filter bank is shown in  FIG. 7 . Here, a band-separating filter bank  701 , a processing section  703  and a band-combining filter bank  702  successively operate on an input digital signal designated as x(n). The processing section  703  may for example perform such operations as data encoding/decoding, echo cancellation processing, etc.  
      The band-separating filter bank  701  divides the input digital signal x(n) into a total of M channels of sub-band signals, whose respective frequency bands will be numbered as bands  0  to (M- 1 ) respectively.  710 ˜ 71   n  designate the respective band-separating filters of the filter bank  701 , respectively corresponding to frequency bands  0  to (M- 1 ), with their respective Z-transform transfer functions (referred to in the following simply as transfer functions) designated as G O  (z)˜G M-1 (z). The output sub-band signals from these filters  710 ˜ 71   n  are supplied to respective ones of a set of decimators  720 ˜ 72   n , with the resultant down-sampled sub-band signals being supplied to the processing section  703 . The band-combining filter bank  702  includes a set interpolators  740 ˜ 74   n  which respectively receive the processed sub-band signals produced from the processing section  703 , while  730 ˜ 73   n  are band-combining filters respectively corresponding to the frequency bands  0 ˜M- 1  and having respective transfer functions K 0 (z)˜K M-1 (z), which receive the corresponding ones of the interpolated sub-band signals which are produced from the interpolators  740 ˜ 74   n.    
      The decimation and interpolation factor is indicated as D. That is to say, one in every D samples of a sub-band signal is selected by the decimation processing, while (D- 1 ) fixed sample values (e.g., zero values) are inserted following each sample of a processed sub-band signal, by the interpolation processing.  
      It will be assumed that the number M of sub-bands into which the input digital signal is divided is identical to the aforementioned decimation and interpolation factor D.  
      The output sub-band signals from the filters  730 ˜ 73   n  are additively combined in an adder  704 , to obtain a digital signal y(n) as the output signal.  
      This is a recovered version of the original digital signal (possibly modified as a result of the operation of the processing section  703 ). If it is assumed that the processing  703  section performs a type of processing such as echo cancellation, which requires the use of DFT filter banks for band separation and combining, then the respective transfer functions G k (z) and K k (z) of the k-th band-separating filter and k-th band-combining filter are expressed as follows by equations (1) and (2) respectively: 
 
 G   k ( z )= G   0 ( zW   M   k )   (1) 
 
 K   k ( z )= W   M   −k   K   0 ( zW   M   k )   (2) 
 
      Here, W M   k =exp(−j2πk/M), with 0&lt;k&lt;M- 1 , and each of G 0 (z) and K 0 (z) represents the transfer function of the prototype filter of a DFT (Discrete Fourier Transform) filter bank. The term “prototype filter” as used herein in relation to a band-separating filter bank or band-combining filter bank signifies a low-pass filter which handles the lowest frequency band, such as filter  710  of the band-separating filter bank  701  in  FIG. 7 .  
      If however the processing section  703  performs processing which requires the use of cosine modulation filter banks as the band-separating filter bank and band-combining filter bank, then the respective transfer functions of the k-th band-separating filter and k-th band-combining filter are obtained as follows from equations (3) and (4) respectively: 
 
 G   k ( z )= a   k   *c   k   P ( zW   2M   (k+1/2) )+ a   k   *c   k   *P ( zW   2M   −(k+1/2) )   (3) 
 
 K   k ( z )= a   k   *c   k   P ( zW   2M   (k+1/2) )+ a   k   *c   k   *P ( zW   2M   −(k+1/2) )   (4) 
 
      Where W 2M =exp(−jπ/M), with 0&lt;k&lt;M- 1 , a k =exp(jθ k ), C k =W 2M   (k+1/2)(N-1)/2 , θ k =(2k+1)π/4, N is the number of taps of the prototype filter, the * symbol indicates the complex conjugate, and P(z) designates the transfer function of the prototype filter of a cosine modulation filter bank.  
      In the prior art, a FIR low-pass filter having a symmetric impulse response is used as the prototype filter in such a type of filter bank. An example of such a symmetric impulse response is shown in  FIG. 8 .  
      However with such a prior art type of apparatus which uses a filter in which each of the prototype filters of the sub-band separating filter bank and sub-band combining filter bank is a FIR (finite impulse response) low-pass filter having a symmetric impulse response, designating the number of taps of such a prototype filter as N, an amount of delay will be produced by the operation of a filter bank that is equal to the total of the group delays of (N- 1 ) taps. In many applications, such an amount of delay becomes a serious disadvantage. For example, if the processing section  703  in  FIG. 7  performs echo canceller processing, then it is essential to minimize the sub-band separating and sub-band combining filter delays, in order to achieve a suitably high speed of control response together with stability of operation.  
     SUMMARY OF THE INVENTION  
      It is an objective of the present invention to overcome the above problem by providing an improved sub-band separating apparatus and sub-band combining apparatus, each apparatus having at least one band-separating filter bank and at least one band-combining filter bank, wherein an amount of delay which results from filtering performed successively by said filter banks is reduced, by comparison with prior art types of filter bank utilized for a sub-band separating and combining apparatus.  
      To achieve the above objective, the invention provides a sub-band separating apparatus and sub-band combining apparatus wherein each of respective basic filters of a band-separating filter bank and a band-combining filter bank is configured to have a symmetric impulse response, to thereby achieve a lower amount of group delay for each prototype filter and thereby reduce an overall amount of delay which results from filtering by the filter banks.  
      The invention further provides a digital signal encoder apparatus comprising sub-band separating means for converting an input digital signal to a plurality of sub-band signals and encoding means for respectively encoding said sub-band signals and combining resultant encoded data into a data stream to be transmitted or processed, in which the sub-band separating means consists of a low-delay sub-band separating apparatus as described above, and similarly provides a corresponding decoder apparatus which utilizes a low-delay sub-band combining apparatus as described above The invention moreover enables such an encoder apparatus and decoder apparatus to each perform efficiently by providing a high-speed algorithm which utilizes the periodicity of a cosine function to minimize an amount of processing which is required to implement the respective functions of the various band-pass filters of such an apparatus  
      Such an encoder apparatus and decoder apparatus are particularly suitable for use in compression encoding and subsequent expansion decoding of a PCM digital audio signal.  
      The invention further enables an improved digital wireless microphone system to be configured, in which a digital audio signal which is to be transmitted by radio as a data stream is compression-encoded by an encoding apparatus utilizing a low-delay sub-band separating apparatus and is subsequently decoded upon reception, by using a decoding apparatus similarly utilizing a low-delay sub-band combining apparatus according to the invention.  
      The apparatus moreover provides an echo canceller apparatus in which a digital audio signal received from a remote location to be audibly reproduced by a loudspeaker is subjected to sub-band separation and then adaptive filtering of the respective sub-band signals, a digital audio signal obtained from a microphone which may be adjacent to the loudspeaker is also converted to a set of sub-band signals, the differences between these signals and the adaptively filtered sub-band signals are obtained as respective error signals and applied to update the coefficients of the adaptive filters, and are also subjected to band-combining filter processing to obtain an output digital signal that is returned to the remote location, in which the sub-band separating and sub-band combining processing are performed using low-delay sub-band separating apparatuses and a low-delay sub-band combining apparatus according to the invention. As a result, due to the reduced amounts of filter delay, more effective suppression can be achieved of a signal that is returned to the remote location as an echo. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a general system block diagram of a digital signal sub-band separating apparatus and sub-band combining apparatus according to a first embodiment of the invention;  
       FIG. 2  is a graph illustrating an asymmetric impulse response of a FIR filter;  
       FIG. 3A  is a graph for comparing respective amplitude/frequency characteristics of a conventional type of FIR low pass filter and of a FIR low pass filter having an asymmetric impulse response;  
       FIG. 3B  is a graph for comparing respective group delay/frequency characteristics of a conventional type of FIR low pass filter and of a FIR low pass filter having an asymmetric impulse response;  
       FIG. 4  is a general system block diagram of an embodiment of a PCM digital audio signal encoder apparatus and decoder apparatus, utilizing a sub-band separating apparatus and sub-band combining apparatus according to the invention, for use in transmitting or storing digital audio signal data in compressed encoded form;  
       FIG. 5  is a general system block diagram of an embodiment of a wireless microphone transmitter system, having a PCM digital audio signal encoder apparatus and decoder apparatus, utilizing a sub-band separating apparatus and sub-band combining apparatus according to the invention;  
       FIG. 6  is a general system block diagram of an embodiment of an echo canceller apparatus which utilizes sub-band separating apparatuses and a sub-band combining apparatus according to the invention;  
       FIG. 7  is a general system block diagram of an example of a prior art sub-band separating apparatus and sub-band combining apparatus; and  
       FIG. 8  is a graph illustrating a symmetric impulse response of a FIR filter as used in the apparatus of  FIG. 7 . 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS  
     First Embodiment  
       FIG. 1  is a general system block diagram of a first embodiment of the invention, which is a combination of a sub-band separating apparatus and a sub-band combining apparatus, for use with a processing (or transmitting/receiving) system. In  FIG. 1 , a band-separating filter bank  1  performs filtering of respective frequency bands of an input PCM digital signal x(n), then decimation is applied, using a decimation factor of D. The band-separating filter bank  1  is formed of a set of band-separating filters  010 ˜ 01   n  and a corresponding set of down-samplers  020 ˜ 02   n,  each of which applies decimation by a fixed factor D (i.e., selecting one in every D successive samples) to the output sub-band signal from the corresponding one of the band-separating filters  010 ˜ 01   n.  After the resultant decimated sub-band signals have been subjected to predetermined processing in a processing section  3 , they are inputted to a band-combining filter bank  2 , which effects interpolation of the signals, i.e., by inserting (D- 1 ) interpolation values for each value of an input signal, and filtering of the resultant interpolated sub-band signals by respective filters. The resultant filtered interpolated sub-band signals are then additively combined by an adder  4 , to recover the original PCM digital signal y(n) or a processed version of that signal.  
      The band-combining filter bank  2  is formed of a set of up-samplers  040 ˜ 04   n  which receive and apply interpolation by the aforementioned factor D to respectively corresponding ones of the sub-band signals which are outputted from the processing section  3 , and a set of band-combining filters  030 ˜ 03   n  respectively corresponding to the frequency bands of the sub-band signals, which receive and filter respectively corresponding ones of the interpolated sub-band signals which are outputted from the up-samplers  040 ˜ 04   n,  with the resultant sub-band signals being supplied to the adder  4 .  
      If the processing section  3  performs a type of processing such as echo cancellation, for which each of the band-separating filter bank  1  and band-combining filter bank  2  should be DFT filter banks, then the respective transfer functions of the k-th band-separating filter of filter bank  1  and the k-th band-combining filter of the filter bank  2  are expressed as follows by equations (5) and (6) respectively: 
 
 H   k ( z )= H   0 ( zW   M   k )   (5) 
 
 F   k ( z )= W   M   −k   F   0 ( zW   M   k )   (6) 
 
      Where W M   k =exp(−j2πk/M), with 0&lt;k &lt;M- 1   
      In equations (5), (6), H 0 (z) and F 0 (z) respectively express the transfer functions of the prototype filters  010 ,  030  respectively of the band-separating filter bank  1  and band-combining filter bank  2  of this embodiment, for the case in which each of these is a DFT filter bank.  
      If the processing section  3  on the other hand performs a type of processing which requires that each of the band-separating filter bank  1  and band-combining filter bank  2  be a cosine modulation filter bank, then transfer functions of the k-th band-separating filter of filter bank  1  and the k-th band-combining filter of the filter bank  2  are expressed as follows by equations (7) and (8) respectively: 
 
 H   k ( z )= e   j θ k   P ( W   2M   (k+1/2)   z )+ e   −j θ k   P ( W   2M   (k−1/2)   z )   (7) 
 
 F   k ( z  )= e   j Ψ k   P ( W   2M   (k+1/2)   z )+ e   −j Ψ k   P ( W   2M   (k−1/2)   z )   (8) 
 
 where 0&lt;k&lt;M- 1 , and where, designating the group delay of the prototype filter as k d , the following relationships are true: 
 
θ k ( z )=( M−k   d )(2 k+ 1)Π/(4 M ) 
 
Ψ k ( z )=(− M−k   d )(2 k+ 1)Π/(4 M ) 
 
      In equations (7)and (8), P(z)expresses the transfer function of the prototype filter of a cosine modulation filter bank, i.e., in this case, the transfer function of each of the prototype filters  010  and  030  of the band-separating filter bank  1  and band-combining filter bank  2  respectively.  
      For encoding efficiency, the decimation/interpolation factor D is preferably made equal to the separation factor M, i.e., made equal to the number of sub-band signal channels.  
       FIG. 2  shows an example of the impulse response of each of the prototype filters  010 ,  030  of this embodiment. As shown, this is an asymmetric impulse response, as opposed to the symmetric impulse response shown in  FIG. 8 .  
      The operation of the sub-band separating/combining apparatus having the configuration set out above will be described referring to  FIG. 1 . The input PCM digital signal x(n) is supplied to the band-separating filter bank  1 , to be subjected to convolution processing in respective frequency bands by the band-separating filters  010 ˜ 01   n,  to be thereby separated into respective sub-band signals which are outputted from these filters.  
      Each of these sub-band signals is then subjected to decimation by the factor D (i.e., through extraction of one out of every D successive samples of a sub-band signal) by the corresponding one of the down-samplers  020 ˜ 02   n.  The resultant decimated sub-band signals are then subjected to some form of signal processing by the processing section  3 , where the term “processing” is to be interpreted as having a broad significance which can for example include encoding a signal for transmission or storage, followed by decoding upon reception or read-out  
      The resultant processed sub-band signals which are produced from the processing section  3  are supplied to respectively corresponding ones of the up-samplers  040 ˜ 04   n  in the band-combining filter bank  2 , and each of the resultant interpolated sub-band signals is then subjected to convolution by the corresponding one of the band-combining filters  030 ˜ 03   n.  The resultant filtered sub-band signals are then additively combined by the adder  4 , to obtain as output a recovered PCM digital signal, i.e., in general, a modified version of the original PCM digital signal x(n), as determined by the processing applied by the processing section  3 .  
       FIG. 3A  shows a comparison between the amplitude/frequency response of a prototype filter (i.e., a FIR low pass filter) having an asymmetric impulse response as utilized with the present invention, as indicated by the full-line curve, and a prototype filter having a symmetric impulse response as used in the prior art, as indicated by the broken-line curve. Both of the filters are formed with 128 taps, and differ only with respect to the impulse response.  
       FIG. 3B  shows a comparison between the group delay/frequency characteristic of a digital signal sub-band separating/combining apparatus such as that of  FIG. 1  (i.e., with respect to the total amount of group delay which occurs from input to a sub-band separating filter bank to output from a sub-band combining filter bank, and results only from the effects of these filter banks), for the case in which both of the filter banks utilizes a prototype filter having an asymmetric impulse response as illustrated in  FIG. 2 , in accordance with the present invention, with that delay/frequency characteristic being shown as a full-line curve, and for the case in which the filter banks each utilize a prototype filter having a symmetric impulse response, as illustrated in  FIG. 8 , with that delay/frequency characteristic being shown as a broken-line curve.  
      As is clear from  FIG. 3A , with this embodiment of the invention, the attenuation/frequency characteristic of the prototype filter is closely similar to that of prior art type of filter used as a prototype filter of a digital signal sub-band separating/combining apparatus. However as can be seen from  FIG. 3B , a significant improvement is obtained with regard to reducing the amount of group delay which is incurred in the separating/combining processing.  
      Thus with this embodiment of the invention, by using a FIR low-pass filter having an asymmetric impulse response as each of the respective prototype filters of a band-separating filter bank and band-combining filter bank of a digital signal sub-band separating/combining apparatus, the amount of overall delay which results from transfer of a digital signal through such an apparatus can be substantially reduced, without causing significant deterioration of the attenuation/frequency characteristic of the apparatus.  
     Second Embodiment  
       FIG. 4  shows a second embodiment of the invention, which is a PCM digital audio signal compression encoding/decoding apparatus. It should be understood that the invention could of course be applied to various other types of digital signal encoding apparatus. In  FIG. 4 , an encoder  101  receives as input a PCM digital audio signal, performs sub-band separating processing, and uses human psycho-acoustic response characteristics etc., to perform compression encoding processing. The encoder  101  is formed of a band-separating filter bank  102 , psycho-acoustic model section  103 , quantization/encoding section  104  and frame forming section  105 .  
      The band-separating filter bank  102  is formed as described hereinabove for the band-separating filter bank  1  of the first embodiment, for the case in which this is a cosine modulation filter bank in which the band-separating filters are configured in accordance with equation (7) above, with a decimation factor D that is identical to the separation factor (i.e., is equal to the number of sub-band signal channels.  
      The bit stream that is produced from the encoder  101  is inputted to the demodulator  106 , in which the original sub-band signals are subjected to dequantization and sub-band combining processing in accordance with the frame information, to thereby recover the original PCM digital audio signal. The demodulator  106  is formed of a frame analyzing section  107 , a dequantization/decoding section  108  and a band-combining filter-bank  109 .  
      The band-combining filter bank  109  is formed as described hereinabove for the band-separating filter bank  1  of the first embodiment, for the case in which this is a cosine modulation filter bank in which the band-separating filters are configured in accordance with equation (8) above, with a decimation factor D that is identical to the number M of sub-band signal channels.  
      The operation of the encoder  101  and demodulator  106  will be described referring to  FIG. 4 . Firstly, a PCM digital audio signal is inputted to the encoder  101 , and is converted to D channels of sub-band signals (i.e., respective sequences of decimated samples) by the band-separating filter bank  102  as described hereinabove for the first embodiment.  
      These sub-band signals are inputted to the quantization/encoding section  104  and the psycho-acoustic model section  103 , to be processed in parallel by these. In the psycho-acoustic model section  103 , the input PCM digital audio signal is subjected to frequency analysis by a method such as FFT processing, etc., to calculate scale factor information from the sub-band signals and to calculate a masking level for the quantization error based on a psycho-acoustic model of human auditory characteristics. Bit allocation information is thereby calculated for each of the frequency bands respectively corresponding to the sub-band signals. However it should be noted that it would be equally possible to calculate only the bit allocation information at this time, without performing FFT processing.  
      In the quantization/encoding section  104 , quantization and encoding are performed in accordance with the bit allocation information which is calculated by the psycho-acoustic model section  103 , and the resultant encoded data are combined with externally supplied ancillary data in the frame forming section  105 , to obtain successive data frames which are outputted from the encoder  101 .  
      These data frames are then transmitted via a transmission path  110  to be inputted to the demodulator  106 . In the demodulator  106 , the frame analyzing section  107  first performs frame analysis to separate out the ancillary data of the frames, and also separates the bit allocation information and the sub-band sample information for the respective sub-bands, from the side information which has been transmitted within the frames. The dequantization/decoding section  108  then recovers the original set of sub-band signals, and these are inputted to the band-combining filter bank  109 . Here, filtering and interpolation of samples are applied to the respective sub-band signals, and additive combining of the resultant sub-band signals, are performed as described hereinabove for the band-combining filter bank  2  of the first embodiment, to recover the original PCM digital audio signal.  
      With this embodiment of the invention, in which the band-separating filter bank  102  and band-combining filter bank  109  each achieve a low amount of group delay, a PCM digital signal compression encoding/decoding apparatus can be realized which has a reduced amount of overall system delay.  
      In the above description, an example is given in which low-delay sub-band separating/combining is performed in the case of PCM digital audio signal compression encoding/decoding. However it would be equally possible to apply the principles described above to a quantization algorithm for modifying images, i.e., to compression encoding and decoding of a digital video signal.  
      Furthermore the invention could be applied to achieve a higher speed of processing for the band-separating and band-combining operations by making the number of taps of each prototype filter twice the separation factor M, i.e., 2M and by converting each of the above equations (5), (6) to the time domain, and making use of the fact that a cosine function within each of the converted equations periodically takes the values 1 and −1 for successive signal samples, as shown in the following. This also will enable the hardware and memory requirements for performing the processing to be reduced. Specifically, equations (5), (6) can be expressed as respective time-axis functions by the following equations (7), (8):  
                 h   k     ⁡     (   n   )       =     2   ⁢       p   L     ⁡     (   n   )       ⁢     cos   ⁡     [         (       2   ⁢   k     +   1     )     ⁢     π     2   ⁢   M       ⁢     (     n   -       k   d     2       )       -       (       2   ⁢   k     +   1     )     ⁢     π   4         ]                 (   7   )                   f   k     ⁡     (   n   )       =     2   ⁢       p   L     ⁡     (   n   )       ⁢     cos   ⁡     [         (       2   ⁢   k     +   1     )     ⁢     π     2   ⁢   M       ⁢     (     n   -       k   d     2       )       +       (       2   ⁢   k     +   1     )     ⁢     π   4         ]                 (   8   )             
 
      In the above, k is a band index, i.e., taking values  0 , 1 , . . . ,M- 1 , h k (n) is the impulse response of the band-separating filter for the k-th sub-band, f k (n) is the impulse response of the band-combining filter for the k-th sub-band, p L (n) is the impulse response of each prototype filter, and k d  is the group delay measured from input to output of the band-separating filter bank or band-combining filter bank.  
      The manner of achieving high-speed processing will be described only for the case of band-separating operation. The band-separating processing can be expressed by the following equation (9):  
                 x   k     ⁡     (   r   )       =       ∑     n   =   0       N   -   1       ⁢         h   k     ⁡     (   n   )       ⁢     x   ⁡     (     rM   -   n     )                   (   9   )             
 
      In the above, x k (r) is the output sub-band signal which results from filtering and decimation of the k-th band, with r expressing respective time-axis positions of the signal samples, N is the number of taps of the filter for the k-th-band, and x(n) is the input signal to the band-separating filter bank, i.e., with n expressing the respective time-axis positions of the input signal samples.  
      Designating n=2M_ 65  +ρ, and inserting the resultant form of equation (7) into equation (9), the following equation (10) can be obtained:  
                 x   k     ⁡     (   r   )       =       ∑     ρ   =   0         2   ⁢   M     -   1       ⁢       ∑     γ   =   0         N     2   ⁢   M       -   1       ⁢         cos   ⁡     [       (       2   ⁢   j     +   1     )     ⁢     π     2   ⁢   M       ⁢     (       2   ⁢   M   ⁢           ⁢   γ     +   ρ   -       k   d     2     -     M   2       )       ]       ·   2     ⁢         p   L     ⁡     (       2   ⁢   M   ⁢           ⁢   γ     +   ρ     )       ·     x   ⁡     (     Mr   -     2   ⁢   M   ⁢           ⁢   γ     -   ρ     )                       (   10   )             
 
      Furthermore, designating the cos term in equation (10) as A, and developing that term A, the following equation (11) can be obtained:  
             A   =       cos   ⁡     [         (       2   ⁢   k     +   1     )     ⁢     π     2   ⁢   M       ⁢     (     ⁢   ρ     -     M   2     -       k   d     2       ]       ·     cos   ⁡     [       (       2   ⁢   k     +   1     )     ⁢   πγ     ]                 (   11   )             
 
      In equation (11), the portion cos(2k+1)πγ takes the value +1 when γ is even = 31  1 when γ is odd. As a result, equation (10) can be rewritten as follows, as equation (12):  
                 x   k     ⁡     (   r   )       =       ∑     ρ   =   0         2   ⁢   M     -   1       ⁢     [       cos   ⁡     [         (       2   ⁢   k     +   1     )     ⁢     π     2   ⁢   M         -     (     ρ   -     M   2     -       k   d     2       )       ]       ·       ∑     γ   =   0         N     2   ⁢   M       -   1       ⁢         (     -   1     )     γ     ·   2   ·       p   L     ⁡     (       2   ⁢   M   ⁢           ⁢   γ     +   ρ     )       ·     x   ⁡     (     Mr   -     2   ⁢   M   ⁢           ⁢   γ     -   ρ     )             ]               (   12   )             
 
      Use of equation (12) as the algorithm for deriving each of the sub-band signals from the input digital signal x(n) enables the band-separation processing to be performed efficiently. A similar algorithm can be utilized for operating on each of the sub-band signals which are to be combined, in the band-combining processing.  
     Third Embodiment  
       FIG. 5  shows the system configuration of a third embodiment of the invention. This is a wireless microphone system which uses sub-band compression encoding/decoding processing having a low amount of delay, implemented as described above for the second embodiment. As a result with this system, by comparison with the prior art, there is a reduced amount of delay between the time at which a sound is received by a microphone of the system and the time at which a corresponding amplified sound is emitted from a loudspeaker.  
      In FIG. a transmitter  200  applies A-D conversion to convert an audio signal from a microphone into a PCM digital audio signal, then applies compression encoding processing as described hereinabove for the second embodiment of the invention, to obtain a compressed bit stream. The bit stream is then subjected to encoding conversion to reduce the effects of errors which may arise when the bit stream traverses a transmission path, and the resultant signal is then applied in digital modulation to obtain a high-frequency modulated signal which is transmitted as radio waves. The transmitter  200  is made up of a microphone  202 , an analog signal amplifier  203 , an A-D converter  204 , a compression encoder  205 , a code conversion/interleaving/error correction circuit  206 , a modulator/amplifier circuit  207  and a transmitting antenna  208 . The compression encoder  205  is is configured in accordance with the second embodiment of the invention.  
      A receiver  201  receives the radio waves which are transmitted from the transmitter  200 , amplifies the resultant signal and applies frequency conversion and demodulation. The resultant demodulated signal is then subjected to transmission path error correction processing, and the resultant encoded compressed signal is decoded to obtain a digital output signal. That digital output signal is then subjected to digital-analog conversion to obtain an analog output audio signal, which can be supplied to drive a transducer such as a loudspeaker (not shown in the drawing). The receiver  201  is made up of a receiving antenna  209 , a high-frequency amplifier/frequency converter  210  coupled to receive a high-frequency signal from the antenna  209 , an intermediate-frequency amplifier  211 , a demodulator  212 , a code conversion/de-interleaving/error correction circuit  213 , a compressed signal decoder  214 , a D-A converter  215  and a analog signal amplifier  216 . The compressed signal decoder  214  is configured in accordance with the second embodiment of the invention.  
      The operation of this digital wireless microphone system is as follows. Firstly, sound waves which reach the microphone  202  are converted to an analog audio signal which is amplified to an appropriate level by the analog signal amplifier  203 , and the resultant signal is converted to a PCM digital audio signal by the A-D converter  204 . In the compression encoder  205 , the PCM digital audio signal is subjected to compression encoding with a low amount of delay, then encoding conversion is applied to reduce the effects of errors arising in the transmission path, by the error correction code conversion circuit  206 , to obtain the final encoded data stream. Various schemes for processing data prior to transmission so that transmission errors can be automatically corrected in the receiving process, such as BCH encoding, interleaving, etc., which could by utilized for the operation of the error correction code conversion circuit  206 .  
      The resultant encoded data stream is sent to the modulator/amplifier circuit  207 , in which it is applied in digital quadrature modulation such as π/4-DQPSK (direct quadrature phase shift keying) modulation, to be converted to a modulated RF signal. This is then amplified to a sufficient level by an amplifier, and supplied to the transmitting antenna  208  to be transmitted as radio waves.  
      In the receiver  201 , the radio waves are received by the receiving antenna 209, the resultant signal is amplified by the high-frequency amplifier/frequency converter  210 , and converted to an intermediate-frequency signal by the high-frequency amplifier/frequency converter  210 , then is amplified by intermediate-frequency (IF) amplifier  211  to a sufficiently high level for performing demodulation. The resultant IF signal is then demodulated by the demodulator  212 . The demodulated signal is subjected to error correction processing to eliminate code errors which may have arisen in the transmission path, by the error correction code conversion section  213 , to obtain an error-corrected signal. The compressed signal decoder  214  then applies low-delay decoding, to recover an original set of sub-band signals, and additive combination of these sub-band signals to recover the original PCM digital audio signal.  
      In some cases it may be possible for the receiving apparatus to directly output only that recovered PCM digital audio signal. However since it may be necessary to drive an analog type of amplifier apparatus such as a high-power audio amplifier, it is preferable to perform D-A conversion so that an analog output signal can also be provided. With this embodiment the PCM digital audio is converted to an analog audio signal by the D-A converter  215 , which is then amplified by the analog signal amplifier  216  to obtain an output analog audio signal.  
      With this embodiment of the invention, a band-separating filter bank and band-combining filter bank each having a low amount of filtering delay are utilized, in a digital signal compression encoding/decoding apparatus. As a result it is possible to implement a digital type of wireless microphone system which enables sounds to be produced in amplified form from a loudspeaker with a minimum of delay between reception of the sounds by a microphone and emission of the sounds from the loudspeaker.  
      Furthermore, when compression encoding is performed using digital modulation, frequency can be effectively utilized, so that it becomes possible to simultaneously use a plurality of wireless microphones.  
     Fourth Embodiment  
       FIG. 6  shows the configuration of an echo canceller which uses sub-band separating/combining processing in accordance with the first embodiment of the invention described above. For the purpose of description, it is assumed that the apparatus shown in  FIG. 6  receives an input digital audio signal x(k) which is transmitted from a distant location (referred to in the following as the far-end location) as a result of speech sound waves that are produced by an individual (referred to in the following as the far-end individual) entering a microphone, with the resultant audio signal being converted to the digital audio signal x(k) and transmitted via some form of communication link. The location of the apparatus shown in  FIG. 6  will be referred to as the near-end location, and will be assumed to be an enclosed room. In  FIG. 6 , numeral  323  denotes a combination of a D/A converter for converting the digital audio signal x(k) to analog form, a loudspeaker, and an audio amplifier which amplifies the analog audio signal to drive the loudspeaker, however for brevity of description that combination will be referred to simply as the loudspeaker  323 . Also in  FIG. 6 , numeral  324  denotes a combination of a microphone and an A/D converter for converting an analog audio signal from the microphone to a digital audio signal, with that combination being referred to in the following simply as the microphone  324 . The purpose of the microphone  324  is to enable an individual at the near-end location to communicate with the far-end individual, however for the purpose of the following description, only those sounds which reach the microphone  324  from the loudspeaker  323  will be considered.  
      The objective of the echo canceller is to prevent sound waves which are emitted from the loudspeaker  323  as a result of the input digital audio signal x(k) and enter the microphone  324  (in accordance with a transfer function of the room at the far-end location, with respect to transmission of sound waves from the loudspeaker  323  to the microphone  324 ) from being transmitted back to the far-end individual in delayed form, as echoes. Basically, the echo canceller estimates the transfer function of the far-end location, and controls a set of adaptive filters accordingly such as to cancel any audio signal components from the microphone  324  that result from the audio signal being applied to the loudspeaker  323 .  
      The echo canceller apparatus is formed of a first band-separating filter bank  320 , whose configuration and operation are as described hereinabove for the band-separating filter bank  1  of the first embodiment, a set of adaptive FIR filters  300 ˜ 30   n  which respectively receive the decimated sub-band signals produced from the band-separating filter bank  320 , a set of coefficient updating sections  310 ˜ 31   n  each of which operates on a corresponding one of the adaptive FIR filters  300 ˜ 30   n  to adjust the tap coefficients of that corresponding filter, a set of adders  330 ˜ 33   n  whose respective outputs are supplied to corresponding ones of the coefficient updating sections  310 ˜ 31   n  and which each receives at a first input thereof an output signal produced from a corresponding one of the adaptive FIR filters  300 ˜ 30   n,  a second band-separating filter bank  321 , whose operation and configuration are also in accordance with the band-separating filter bank  1  of the first embodiment and which receives the aforementioned digital audio signal produced from the microphone  324  and inputs each of the resulting decimated sub-band signals to a subtraction input of a corresponding one of the adders  330 ˜ 321 , a band-combining filter bank  322  whose operation and configuration are in accordance with the band-combining filter bank  2  of the first embodiment and which receives respectively outputs produced from the adders  330 ˜ 321 , and an adder  340  which additively combines the interpolated sub-band signals which are produced from the band-combining filter bank  322  to obtain a digital audio output signal y(n), to be transmitted back to the far-end location via a communication link.  
      Each of the band-separating filter banks  320  and  321  and the band-combining filter bank  322  is configured with a prototype filter which is a FIR low-pass filter having an asymmetric impulse response, with each of the band-separating filter banks  320 ,  321  being a DFT filter bank which is formed in accordance with equation (5) above and with the band-combining filter bank  322  being a DFT filter bank which is formed in accordance with equation (6) above.  
      The operation of this echo canceller apparatus is as follows. The input audio signal which is sent from the far-end individual passes over a transmission path and arrives as the digital audio signal x(k) which is supplied to the band-separating filter bank  320  and to the loudspeaker  323 . In the band-separating filter bank  320 , the input signal is subjected to convolution processing in respective frequency bands by the band filters, and the resultant signals are subjected to decimation processing by a decimation factor D which is no greater than the separation factor M, as described for the first embodiment. The resultant down-sampled sub-band samples are inputted to the adders  330 ˜ 33   n.  Sound waves which are emitted by the loudspeaker  323  are received by the microphone  324 , and the resultant audio signal is inputted to the band-separating filter bank  321 .  
      In the band-separating filter bank  321 , the input signal is subjected to convolution processing in respective frequency bands by the band filters, and the resultant sub-band signals are subjected to decimation processing by a decimation factor D which is no greater than the separation factor M, as described for the first embodiment. The resultant down-sampled sub-band signals are inputted to respectively corresponding ones of the adaptive FIR filters  300 ˜ 30   n.  The resultant output signal from each of the adaptive FIR filters  300 ˜ 30   n  has the corresponding one of the sub-band signals from the band-separating filter bank  320  subtracted therefrom, in the corresponding one of the adders  330 ˜ 33   n,  to thereby obtain an error signal. These error signals are inputted to respectively corresponding ones of the coefficient updating sections  310 ˜ 31   n,  and also inputted to respectively corresponding ones of the up-converters of the band-combining filter bank  322 . Thus, the signal y(n) which is obtained from the band-combining filter bank  322  will be reduced in amplitude in accordance with reduction of the error signals.  
      A known type of coefficient updating algorithm such as the NLMS algorithm can be utilized for the operation of each of the coefficient updating sections  310 ˜ 31   n.  Such an algorithm is of a type whereby, at each sample time point of the input digital signal to a FIR filter, the coefficients of the filter are updated by adding thereto an updating amount, which is determined in accordance with a preceding history of errors between the actual output values produced from the filter and respective ideal values which would be produced by an ideal FIR filter. With a LMS (least mean-square) type of adaptive algorithm, only the error resulting from the immediately preceding digital signal input to the filter is utilized, in general, with the updating being successively performed starting from an initial assumed set of coefficients (e.g., all zero). The coefficients of a filter are processed as a vector quantity, as are each of the digital signal values.  
      Basically, designating successive input signal sample time points as  0 , 1  . . . k, (k+), and the corresponding values of the sets of coefficients of a filter as the vectors w( 0 ), w( 1 ) . . . w(k), w(k+ 1 ), . . . , e.g., with w( 0 ) being predetermined as zero, and designating as δw(k)an updating amount, each of successive coefficient values w(k+1) are obtained as: 
 
 w ( k+   1 )= w ( k )+μ.δ w ( k )   (13) 
 
      Here, μ is an adaptation constant, generally referred to as the step size, which controls the size of the updating amount, at each update. The updating amount δw(k) is derived based on an amount of error between the preceding output value w(k) from the filter and the output which would have been produced from an ideal filter, which can be considered as being identical to the value of the target signal at that time (i.e., with this embodiment, the output value of the corresponding one of the sub-band signals from the sub-band separating filter bank  321  at that time).  
      With the NLMS (normalized least mean-square) method, the step size is normalized, i.e., is automatically adjusted based on the power of the input signal to the filter. Typically, the NLMS algorithm may be expressed as follows: 
 
 W ( k+   1 )= w ( k )+(α/( x ( k ) T   x ( k )+β)) e ( k ) x ( k )   (14) 
 
      Here, α determines the maximum step size (0&lt;α&lt;2), D is a small-magnitude value for the purpose of preventing division by zero, x(k) is the (preceding) input signal value to the filter, e(k) is the aforementioned error amount between the target signal and the signal resulting from the adaptive filtering of the preceding input signal value, and superscript T denotes the transposed matrix.  
      With this embodiment, the sub-band signals of respective frequency bands which are produced from the band-separating filter bank  320  are subjected to convolution processing by respectively corresponding ones of the adaptive filters  300 ˜ 30   n,  with updating of the filter coefficients being performed for each of these by the corresponding one of the coefficient updating sections  31   n  as described above, and the resultant error signals respectively corresponding to these filtered sub-band signals from the adaptive filters, obtained from the adders  330 ˜ 33   n,  are inputted to the band-combining filter bank  322 . In the band-combining filter bank  322 , these signals are subjected to interpolation processing, using the same interpolation factor D as the factor M used for band separation, and convolution with the band-combining filters is then applied for the respective frequency bands.  
      The additive combination of the resultant signals is then obtained by the adder  340 , as the digital audio signal y(n), which is the output signal from the echo canceller. That signal is transmitted over a communication link to the far-end individual.  
      With this embodiment, due to the fact that each of the filter banks is configured to utilize a FIR low-pass filters having an asymmetric impulse response as the prototype filter, thereby achieving a lower amount of group delay for each of the filter banks than is possible in the prior art, it is found that greater effectiveness can be achieved in suppressing a spurious digital audio signal that may be produced as a component of the output signal y(n) due to sound waves from the loudspeaker  323  reaching the microphone  324 , and thereby returned to the far-end individual. Hence, greater effectiveness in echo suppression can be achieved than is possible in the prior art.  
      It should be noted that although the invention has been described in the above referring to specific embodiments, it should be understood that various modifications to the described embodiments could be envisaged, which fall within the scope claimed for the invention in the appended claims.