Abstract:
For purposes of noise suppression, spectral subtraction filtering is performed in sample-wise fashion in the time domain using a time-domain representation of a spectral subtraction gain function computed in block-wise fashion in the frequency domain. By continuously performing time-domain filtering on a sample by sample basis, the disclosed methods and apparatus avoid block-processing delays associated with frequency-domain based spectral subtraction systems. Consequently, the disclosed methods and apparatus are particularly well suited for applications requiring very short processing delays. Moreover, since the spectral subtraction gain function is computed in a block-wise fashion in the frequency domain, high quality performance in terms of reduced tonal artifacts and low signal distortion is retained.

Description:
RELATED APPLICATIONS 
     The present application is related to pending U.S. patent application Ser. No. 09/084,387, filed May 27, 1998 and entitled Signal Noise Reduction by Spectral Subtraction using Linear Convolution and Causal Filtering. The present application is also related to pending U.S. patent application Ser. No. 09/084,503, also filed May 27, 1998 and entitled Signal Noise Reduction by Spectral Subtraction using Spectrum Dependent Exponential Gain Function Averaging. Each of the above cited pending patent applications is incorporated herein in its entirety by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to communications systems, and more particularly, to methods and apparatus for mitigating the effects of disruptive background noise components in communications signals. 
     BACKGROUND OF THE INVENTION 
     Today communications are conducted in a wide variety of potentially disruptive environments, and modern communications solutions are therefore often equipped to compensate for such environments. For example, the microphone in a typical landline or mobile telephone will often pick up not only the voice of the near-end telephone user, but also any surrounding near-end background noise which may be present. This is particularly true in the context of office and automobile handsfree solutions. Since such background noise can be annoying or even intolerable to the far-end user, many of today&#39;s telephones are equipped with noise reduction processors which attempt to suppress the background noise while permitting the speaker&#39;s voice to pass through without distortion. Such noise reduction processors are often based on the well known technique of spectral subtraction in which the spectral content of a noisy speech signal is analyzed, and those frequency components having poor signal-to-noise ratios are attenuated. See, e.g., S. F. Boll, Suppression of Acoustic Noise in Speech using Spectral Subtraction,  IEEE Trans. Acoust. Speech and Sig. Proc.,  27:113-120, 1979. 
     When implementing a noise reduction processor, it is important to minimize any artifacts or delay which might be introduced, as such artifacts and delay can be as bothersome to the far-end user as is the background noise. 
     Accordingly, the above incorporated patent applications disclose spectral subtraction noise reduction systems which introduce low signal distortion as compared to conventional spectral subtraction techniques. Specifically, pending application Ser. No. 09/084,387 discloses a block-based spectral subtraction noise reduction processor in which signal filtering is carried out in the frequency domain using a reduced-variance, reduced-resolution gain function filter. Advantageously, the order of the gain function is chosen such that the frequency-domain filtering corresponds to a true, non-circular convolution in the time domain, and a phase is added to the gain function so that the gain function is causal. As a result, the disclosed noise reduction processor introduces fewer tonal artifacts and fewer inter-block discontinuities as compared to conventional spectral subtraction techniques. Moreover, pending application Ser. No. 09/084,503 discloses techniques for further reducing the variance of the filter gain function and for thereby further reducing the introduction of tonal artifacts. Specifically, the filter gain function is averaged across blocks, for example in dependence upon a measured discrepancy between the spectral density of the noisy speech signal and the spectral density of the noise alone. 
     While the frequency-domain spectral subtraction filtering techniques of application Ser. Nos. 09/084,387 and 09/084,503 work particularly well in the context of block-based systems (i.e., systems such as the well known Global System for Mobile Communication, or GSM, in which signals are by definition processed sample-block by sample-block), the block-processing times associated with those techniques may not be suitable for applications requiring extremely short signal processor delays. For example, in wire-phone systems, the maximum tolerable signal delay can be as short as 2 ms (corresponding to 16 samples at the standard 8 kHz telephone sampling rate). Consequently, there is a need for improved methods and apparatus for performing noise reduction by spectral subtraction. 
     SUMMARY OF THE INVENTION 
     The present invention fulfills the above-described and other needs by providing noise reduction techniques in which spectral subtraction filtering is performed in sample-wise fashion in the time domain using a time-domain representation of a spectral subtraction gain function computed in block-wise fashion in the frequency domain. By continuously performing time-domain filtering on a sample by sample basis, the disclosed methods and apparatus can avoid the block-processing delays associated with frequency-domain based spectral subtraction systems. As a result, the disclosed methods and apparatus are particularly well suited for applications requiring very short processing delays. Moreover, since the spectral subtraction gain function is computed in a block-wise fashion in the frequency domain (e.g., using the techniques of the above incorporated co-pending application Ser. Nos. 09/084,387 and 09/084,503), high quality performance in terms of reduced tonal artifacts and low signal distortion is retained. In applications where only stationary, low-energy background noise is present, computational complexity can be reduced by generating a number of separate spectral subtraction gain functions during an initialization period, each gain function being suitable for one of several predefined classes of input signal (e.g., for one of several predetermined signal energy ranges), and thereafter fixing the several gain functions until the input signal characteristics change. 
     In an exemplary embodiment, a noise reduction processor includes a time-domain filter configured to convolve a noisy input signal with a time-domain spectral subtraction gain function to provide a noise reduced output signal, a spectral subtraction gain function processor configured to compute a frequency-domain spectral subtraction gain function as a function of the noisy input signal, and a transform processor configured to provide the time-domain spectral subtraction gain function by transforming the frequency-domain spectral subtraction gain function. Advantageously, the time-domain filter can continuously convolve the noisy input signal with a prevailing time-domain spectral subtraction gain function, and the prevailing time-domain spectral subtraction gain function can be periodically updated by the transform processor. As a result, the exemplary noise reduction processor can provide extremely short delay times between the noisy input and noise-suppressed output signals. Moreover, samples of the noisy input signal can be delayed prior to being convolved with the time-domain spectral subtraction gain function so that the sound quality of the noise-suppressed output signal can be adjusted. Additionally, a minimum phase can be added to the frequency-domain spectral subtraction gain function to provide a causal time-domain filter having a short delay. 
     The above-described and other features and advantages of the invention are explained in detail hereinafter with reference to the illustrative examples shown in the accompanying drawings. Those of skill in the art will appreciate that the described embodiments are provided for purposes of illustration and understanding and that numerous equivalent embodiments are contemplated herein. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an exemplary noise reduction system according to the invention. 
     FIG. 2 is a block diagram of an exemplary spectral subtraction gain function processor which can be used in the system of FIG.  1 . 
     FIG. 3 is a block diagram of an alternative noise reduction system according to the invention. 
     FIG. 4 is a block diagram of an exemplary gain function processor which can be used in the system of FIG.  3 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 depicts an exemplary noise reduction system  100  according to the present invention. As shown, the exemplary system  100  includes a delay buffer  110 , a frame buffer  120 , a frequency-domain spectral subtraction gain function processor  130 , an Inverse Fast Fourier Transform (IFFT) processor  140 , and a time-domain spectral subtraction filter  150 . Those of skill in the art will appreciate that the below described functionality of the various blocks of the system  100  of FIG. 1 can be implemented in practice using any of a variety of known hardware configurations, including a general purpose digital computer, standard digital signal processing components and one or more application specific integrated circuits. 
     In FIG. 1, a noisy speech signal x(n) is coupled to an input of the delay buffer  110  and to an input of the frame buffer  120 . An output of the delay buffer  110  is coupled to a signal input of the time-domain spectral subtraction filter  150 , and an output of the frame buffer  120  is coupled to a signal input of the frequency-domain gain function processor  130 . An output of the gain function processor  130  is coupled to an input of the IFFT processor  140 , and an output of the IFFT processor  140  is coupled to a gain function input of the time-domain filter  150 . The filter  150  provides a noise-suppressed speech signal y(n). 
     In operation, successive samples of the noisy speech signal x(n) (e.g., a near-end microphone signal including near-end background noise) are fed to the delay buffer  110  and to the frame buffer  120 . The frame buffer  120  collects the incoming samples and passes them, a frame at a time, to the gain function processor  130  (where a frame is understood to be a collection of an integer number L of consecutive signal samples). Additionally, the delay buffer  110  introduces an adjustable delay of zero to L samples and passes the delayed samples, one at a time, to the time-domain spectral subtraction filter  150 . The spectral subtraction filter  150  continually convolves the delayed samples with a prevailing time-domain spectral subtraction gain function {tilde over (g)} M (i) (where M is an integer sub-frame length and i is an integer frame count as described in detail below) to provide the noise-reduced speech signal y(n). The M-sample time-domain gain function {tilde over (g)} M (i) can therefore be thought of as the impulse response of the time-domain filter  150 , as is well known in the art. 
     According to the invention, the time-domain gain function {tilde over (g)} M (i) is computed on a per-frame basis by the gain function processor  130  and the IFFT processor  140 . More specifically, for each frame i, the gain function processor  130  uses the frame samples X L (i) to compute an M-bin frequency-domain spectral subtraction gain function {tilde over (G)} M (f,i) (as is described in detail below), and the IFFT processor  140  converts the frequency-domain gain function {tilde over (G)} M (f,i) to a corresponding time-domain gain function {tilde over (g)} M (i) which is then used to update the impulse response of the time-domain filter  150  (i.e., the previously existing filter coefficients {tilde over (g)} M (i−1) are replaced with the newly computed coefficients {tilde over (g)} M (i)). However, since the filter  150  continually operates on noisy speech samples using the prevailing gain function, the signal delay between the noise-suppressed output y(n) and the noisy input x(n) is determined only by the delay buffer  110  and the filter  150 , and not by the frame buffer  120 , the gain function processor  130  or the IFFT processor  140 . 
     The above described operation of the exemplary system  100  of FIG. 1 can be contrasted with operation of spectral subtraction systems (such as those described in the above incorporated patent application Ser. Nos. 09/084,387 and 09/084,503) in which filtering is carried out in the frequency domain. In such systems, a frequency-domain representation of a frame of noisy speech samples is multiplied by a frequency-domain gain function (corresponding to convolution in the time domain) to provide a frequency-domain representation of the noise-reduced output signal which is then converted back to the time domain. As a result, the delay between corresponding samples of the noisy speech signal x(n) and the noise-reduced output signal y(n) is as much as one frame period (since all samples in an input frame are processed together to provide a corresponding output frame) plus the overall frame processing time (i.e., the time required to convert a frame of noisy speech samples from the time domain to the frequency domain, then compute the frequency-domain gain function, carry out the frequency-domain multiplication, and convert the result back to the time domain). 
     Advantageously, the exemplary system of FIG. 1 permits the signal delay to be set for best results given a particular application. For example, in applications where signal delay is less critical, the delay buffer  110  can be set to introduce a delay of one frame period so that each sample of the noisy speech signal x(n) is filtered using a gain function computed based on that sample. Doing so renders operation of the system  100  of FIG. 1 equivalent to that of the above incorporated application Ser. Nos. 09/084,387 and 09/084,503 and provides optimal sound quality. Alternatively, in applications where short signal delay is critical, the delay buffer  110  can be set to introduce little or no delay so that each sample of the noisy speech signal x(n) is filtered using a gain function computed based on recently preceding samples. Though sound quality may be slightly diminished, extremely short signal delay is achieved. The trade-off between sound quality and signal delay will be a matter of design choice for each particular application. 
     To ensure that the time-domain filtering performed by the filter  150  is equivalent to frequency-domain filtering, care must be taken when constructing the frequency-domain spectral subtraction gain function {tilde over (G)} M (f,i). Appropriate methods for constructing the frequency-domain gain function (i.e., for implementing the gain function processor  130  of FIG. 1) are described in detail in the above incorporated application Ser. Nos. 09/084,387 and 09/084,503. Briefly, spectral subtraction is built upon the assumption that the speech signal and the background noise signal are random, uncorrelated, and added together to form the noisy speech signal x(n). In other words, if s(n), w(n) and x(n) are stochastic short-time stationary processes representing speech, noise, and noisy speech, respectively, then: 
     
       
           x ( n )= s ( n )+ w ( n ) 
       
     
     and 
     
       
           R   x ( f )= R   s ( f )+ R   w ( f ), 
       
     
     where fε[0, N−1] is a discrete variable corresponding to one frequency bin, and R (*) (f) denotes the power spectral density of a random process. 
     The short-time spectral density is then estimated using, for example, the well known Bartlett method as follows:                R   ^       x   ,   M                       (     f   ,   i     )       =       M   L                       ∑     p   =   0         L   M     -   1                              ℱ        {       x     L   ,   p                       (   i   )       }            2           ,                          
     where X L,p (i) is the ith L-length frame with sub-frames p of M data samples each. This method of computation reduces the variance as well as the frequency resolution of the resulting spectrum. In practice, the trade off between variance reduction and resolution is a matter of design choice, and experiments have shown that a resolution of M=64 frequency bins typically provides quality results. 
     To simplify notation, P x,M (f,i)={square root over ({circumflex over (R)})} x,M (f,i) is defined as the magnitude spectrum estimate. The short-time noise magnitude spectrum can thus be estimated during speech pauses by              P   _       w   ,   M                       (     f   ,   i     )       =     {               μ                     P   ⇀       w   ,   M                       (     f   ,     i   -   1       )       +       (     1   -   μ     )                     P     x   ,   M                       (     f   ,   i     )         ,         noise                   P   _       w   ,   M                       (     f   ,     i   -   1       )       ,           speech   ,                                    
     where μ is an exponential averaging time constant. To detect speech pauses, a Voice Activity Detector (VAD) can be used, as is well known in the art. 
     The expression for the frequency-domain gain function is then given by              G   M                     (     f   ,   i     )       =       (     1   -     k   ·           P   _       w   ,   M     a                     (     f   ,   i     )           P     x   ,   M     a                     (     f   ,   i     )             )       1   a         ,                          
     where k controls the degree of subtraction and a controls whether magnitude or power spectral subtraction is used. The combination of the parameters k and a thus controls the amount of noise reduction. 
     To further reduce the variability of the gain function, the raw frequency-domain gain function G M (f,i) can be adaptively averaged to yield a smoothed frequency-domain gain function {overscore (G)} M (f,i). For example, the adaptation can be made dependent upon a spectral discrepancy between the noise spectra and the noisy speech spectra. Doing so tends to increase the averaging as the input signal becomes more stationary and thereby provides reduced variability of the gain function for stationary noise and low energy speech. 
     To facilitate a causal filter with a short delay, a minimum phase can be imposed on the calculated zero-phase gain function {overscore (G)} M (f,i) to yield the final frequency-domain gain function {tilde over (G)} M (f,i). This can be implemented, for example, using a Hilbert transform relation. See, for example, A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Inter. Ed., 1989. 
     The above described computation of the frequency-domain gain function {tilde over (G)} M (f,i) is depicted in FIG. 2, wherein an exemplary frequency-domain gain function processor  200  is shown to include a voice activity detector  210 , a spectrum estimation processor  220 , a noise averaging processor  230 , a frequency-domain gain function calculation processor  240 , a spectrum discrepancy analyzer  250 , an adaptive averaging processor  260 , and a phase processor  270 . The exemplary gain function processor  200  of FIG. 2 can be used, for example, to implement the frequency-domain gain function processor  130  of FIG.  1 . Those of skill in the art will appreciate that the below described functionality of the various blocks of the system  200  of FIG. 2 can be implemented in practice using any of a variety of known hardware configurations, including a general purpose digital computer, standard digital signal processing components and one or more application specific integrated circuits. 
     In FIG. 2, a frame of noisy speech samples is input to the spectrum estimation processor  220 , and an output of the spectrum estimation processor  220  is switchably coupled to an input of the noise averaging processor  230  under the control of the voice activity detector  210 . The output of the spectrum estimation processor  220  is also coupled to an input of each of the gain function calculation processor  240  and the spectrum discrepancy processor  250 , as is an output of the noise averaging processor  230 . Outputs of the gain function calculation processor  240  and the spectrum discrepancy processor  250  are coupled to respective inputs of the adaptive averaging processor  260 , and an output of the adaptive averaging processor  260  is coupled to an input of the phase processor  270 . The phase processor  270  provides the frequency-domain gain function (e.g., for input to the IFFT processor  140  of FIG.  1 ). 
     In operation, the spectrum estimation processor  220  generates an M-length estimate {overscore (P)} x,M (f,i) of the spectral density of the ith frame of the noisy speech signal x(n). Additionally, during speech pauses, the voice activity detector  210  couples the output of the spectrum estimation processor  220  to the noise averaging processor  230 , and the noise averaging processor averages (e.g., using exponential averaging) the noisy speech spectrum estimate. Since, during speech pauses, the output of the spectrum estimation processor  220  is an estimate of the spectral density of the noise alone, the noise averaging processor  230  provides an averaged estimate {overscore (P)} w,M (f,i) of the spectral density of the background noise w(n). 
     The gain function calculation processor  240  then uses both the noisy speech spectrum estimate {overscore (P)} x,M (f,i) and the averaged noise spectrum estimate {overscore (P)} w,M (f,i), in conjunction with the empirically determined parameters a and k defined above, to compute the raw frequency-domain gain function G M (f,i). Additionally, the spectrum discrepancy processor  250  determines a degree of difference between the spectrum estimates {overscore (P)} w,M (f,i), {overscore (P)} w,M (f,i), the degree of difference being used by the adaptive averaging processor  260  to average (e.g., using exponential averaging with a variable memory) the raw gain function G M (f,i) to provide the averaged, or smoothed gain function {overscore (G)} M (f,i) (see the above incorporated application Ser. Nos. 09/084,387 and 09/084,503 for additional detail regarding the implementation and advantages of gain function averaging based on spectral discrepancy). Thereafter, the phase processor  270  imposes a minimum phase on the averaged gain function {overscore (G)} M (f,i) to provide the final frequency-domain gain function {tilde over (G)} M (f,i) (again, see the above incorporated application Ser. Nos. 09/084,387 and 09/084,503 for additional detail regarding the implementation and advantages of imposing gain function phase). 
     Once the final frequency-domain gain function {tilde over (G)} M (f,i) has been computed, it is transformed (e.g., by the IFFT processor  140  of FIG. 1) to provide an updated time-domain gain function {tilde over (g)} M (i) (e.g, for the filter  150  of FIG.  1 ). As noted above, the noise-reduced output signal y(n) is obtained by convolving the noisy input signal x(n) with the prevailing time-domain gain function {tilde over (g)} M (i) as:          y                   (   n   )       =       ∑     m   =   0       M   -   1                       x                     (     n   -   m     )     ·       g   ~       M   ,   m                           (   i   )     .                                
     Empirical studies have shown that the observed filtering delay is typically in the range of 0 to 8 samples, where the delay is defined as the mass center of the filter along the time axis (since a group delay measure cannot be used for broadband speech signals). Parameter settings of k=0.7, a=1, L=256 and M=64 provide noise reduction of approximately 10 dB. 
     Although the above described technique is not computationally complex, further reductions in complexity can be realized in situations where only relatively low-energy noise is expected. In particular, when a stationary low-energy noise is disturbing the speech signal, empirical studies have shown that only a small number of fixed gain functions are required to provide good speech quality. In other words, one of a finite number of gain functions, each gain function being specifically tailored for one of an equal number of predefined signal classes (e.g., based on signal energy levels corresponding to high-energy vocal sounds, fricatives, stop sounds, etc.), can be dynamically selected based on a determination of the prevailing signal class. Consequently, continual re-computation of the filter gain function can be avoided. Advantageously, the present invention provides methods and apparatus for establishing, or extracting, suitable sets of fixed filter gain functions. 
     Generally, the above described gain function computation techniques are used, during a processor initialization period, to generate the fixed filter gain functions. More specifically, for each frame during the initialization period, the noisy speech signal is classified, and a gain function assigned for use by that signal class is trained, or updated (e.g., by exponential averaging with a gain function computed as described above). At the end of the initialization period (e.g., when small iterative changes indicate that the gain function assigned to each class has reached a reasonably steady state), the gain functions are frozen and thereafter selectively used to filter the noisy speech signal. In other words, for each post-initialization frame, the noisy speech signal is classified, and the corresponding fixed filter gain function is used to filter the noisy speech. 
     Advantageously, the fixed filter gain functions need be re-trained, or re-extracted, only when the signal characteristics change (i.e., when the background noise changes). Such noise changes can be detected during speech pauses by pseudo random tests of the spectral shape of the noise (e.g., by monitoring changes in the amplitude spectral estimate of the noise). Alternatively, the fixed filters can be re-extracted by resuming averaging when too great a discrepancy is detected between the presently selected fixed gain function and a dynamically computed gain function (e.g., computed using the above described techniques). Moreover, the fixed filters can be re-extracted by resuming the averaging function at some predetermined or variable rate (e.g., so many instances per second). 
     Signal classification can be carried out in a number of ways. For example, the noisy speech signal can be classified as belonging to one of several predefined energy-level regions. If so, the energy level e(n) of the noisy speech signal x(n) can be calculated using an exponential averaging as follows: 
     
       
           e ( n )= e ( n− 1)·γ+ x ( n ) 2 ·(1−γ), 
       
     
     where γ is the averaging time constant or memory. The signal energy class e class (n) can then be determined as            e   class                     (   n   )       =     {             1   ,             e                   (   n   )       &lt;       e   level                     (   0   )                   2   ,               e   leverl                     (   0   )       &lt;     e                   (   n   )       &lt;       e   level                     (   1   )                 …                         T   ,               e   level                     (     T   -   1     )       &lt;     e                   (   n   )               .                              
     During initialization, each per-class gain function {overscore (G)} M (f,t,i) (tε[0, T]) can then be averaged in the frequency domain as 
     
       
           {overscore (G)}   M ( f,t,i )= {overscore (G)}   M ( f,t,i− 1)·δ t   +G   M ( f,i )·(1−δ t ), 
       
     
     where δ t  is the per-class averaging time constant and G M (f,i) is the raw frequency-domain gain function described above. 
     After initialization, a specific fixed filter {overscore (G)} M (f,t,i) is selected when the signal class it was designed for is detected. To minimize the delay of the filtering, a minimum phase is imposed on the filter, as described above, to provide a final frequency-domain filter {tilde over (G)} M (f,i). The final frequency-domain filter {tilde over (G)} M (f,i) is converted to the time domain to provide the desired time-domain filter {tilde over (g)} M (i). 
     The above described fixed-filter techniques can be implemented, for example, using the exemplary noise reduction system  300  of FIG.  3 . As shown, the system  300  includes the frame buffer  120 , the IFFT processor  140 , and the time-domain spectral subtraction filter  150  of FIG. 1, as well as a signal classification processor  305  and an alternative spectral subtraction gain function processor  330 . Those of skill in the art will appreciate that the below described functionality of the various blocks of the system  300  of FIG. 3 can be implemented in practice using any of a variety of known hardware configurations, including a general purpose digital computer, standard digital signal processing components and one or more application specific integrated circuits. 
     In FIG. 3, the noisy speech signal x(n) is coupled to an input of each of the frame buffer  120 , the signal classification processor  305 , and the time-domain filter  150 . Outputs of the frame buffer  120  and the signal classification processor  305  are coupled to inputs of the alternative gain function processor  330 , and an output of the gain function processor  330  is coupled to an input of the IFFT processor  140 . An output of the IFFT processor  140  is coupled to a gain function input of the time-domain filter  150 , and the time-domain filter  150  provides the noise suppressed output signal y(n). 
     At a high level, the system  300  of FIG. 3 works much like the system  100  of FIG.  1 . Specifically, the time-domain filter  150  continually processes samples of the noisy speech signal, while the frame buffer  120  collects noisy speech samples and passes them, one frame at a time, to the gain function processor  330 . The gain function processor  330  computes a frequency-domain gain function {tilde over (G)} M (f,i) in frame-wise fashion, and the IFFT processor  140  transforms the frequency-domain gain function to provide a time-domain gain function {tilde over (g)} M (i) which is used to update the taps of time-domain filter  150 . Unlike the system  100  of FIG. 1, however, the system  300  of FIG. 3 uses the signal classification processor  305  to determine which of several predefined classes best describes the current noisy speech sample (e.g., according to the above described energy-level classification scheme). The signal classification processor  305  then provides a class number (i.e., tε[0, T]) to the gain function processor  330  for use in frame-wise computing the frequency-domain gain function {tilde over (G)} M (f,i) as described above (i.e., by extracting T fixed filters during an initialization period and thereafter selecting the appropriate one of the T fixed filters based upon the output of the signal classification processor). 
     FIG. 4 depicts an exemplary frequency-domain gain function processor  400  which can be used to implement the gain function processor  330  of FIG.  3 . As shown, the processor  400  includes the voice activity detector  210 , the spectrum estimation processor  220 , the noise averaging processor  230 , the gain function calculation processor  240 , and the phase processor  270  of FIG. 2, as well as a number of filter extractors  405  and an equal number of filter averaging processors  415 . Those of skill in the art will appreciate that the below described functionality of the various blocks of the system  400  of FIG. 4 can be implemented in practice using any of a variety of known hardware configurations, including a general purpose digital computer, standard digital signal processing components and one or more application specific integrated circuits. 
     In FIG. 4, a frame of noisy speech samples is coupled to an input of the spectrum estimation processor  220 , and an output of the spectrum estimation processor  220  is switchably coupled to an input of the noise averaging processor  230  under the control of the voice activity detector  210 . The output of the spectrum estimation processor  220  is also coupled to an input of the gain function calculation processor  240 , as is an output of the noise averaging processor  230 . Output of the gain function calculation processor  240  is switchably coupled to one of the several filter extractors  405  (e.g., in dependence upon the output of the signal classification processor  305  of FIG.  3 ), and an output of each of the filter extractors  405  is coupled to an input of a respective one of the several averaging processors  415 . Input of the phase processor  270  is selectively coupled to an output of one of the averaging processors  415  (e.g., also in dependence upon the output of the signal classification processor  305  of FIG.  3 ), and the phase processor  270  provides a frequency-domain gain function as output. 
     In operation, the voice activity detector  210 , the spectrum estimation processor  220 , the noise averaging processor  230 , and the gain function calculation processor  240  function as described above with respect to the system  200  of FIG.  2 . However, in the system  400  of FIG. 4, spectrum-dependent exponential gain function averaging is not used to smooth the raw frequency-domain gain function across frames. Instead, the instantaneous frequency-domain gain function G M (f,i) is used during initialization to update a selected one (e.g., as indicated by the signal class number t provided by the signal classification processor  305 ) of the per-class gain functions  405  as is described above. 
     Specifically, the averaging processor  415  associated with the selected filter  405  exponentially averages the instantaneous frequency-domain gain function G M (f,t,i) with the previously existing selected-filter gain function {overscore (G)} M (f,t,i−1) to provide an updated selected-filter gain function {overscore (G)} M (f,t,i). Thus, at the end of the initialization period, the processor  400  has extracted T fixed filter gain functions {overscore (G)} M (f,t,i) and further updating is frozen unless the character of the background noise changes. After initialization, the appropriate fixed-filter gain function {overscore (G)} M (f,t,i) is merely selected in accordance with the signal class number provided by the signal classification processor  305 . 
     During and after initialization, the phase processor  270  adds a minimum phase, as described above with respect to FIG. 2, to provide the final frequency-domain gain function {tilde over (G)} M (f,i). The final frequency-domain gain function {tilde over (G)} M (f,i) is then transformed (e.g., by the IFFT processor  140  of FIG. 3) to provide the updated time-domain gain function {tilde over (g)} M (i) (e.g, for the filter  150  of FIG.  3 ). As before, the noise-reduced output signal y(n) is obtained by convolving the noisy speech signal x(n) with the prevailing time-domain gain function {tilde over (g)} M (i), and the signal delay between input and output is low (typically about 8 samples). 
     Generally, the present invention provides methods and apparatus for performing short-delay noise suppression by spectral subtraction. In exemplary embodiments, signal filtering is performed in sample-wise fashion in the time-domain using a time-domain representation of a spectral subtraction gain function which is computed in frame-wise fashion in the frequency domain. A minimum phase is imposed on the frequency-domain gain function, prior to conversion to the time domain, so that the corresponding time-domain gain function is causal and introduces a minimal filtering delay. The result is good sound-quality noise reduction with a typical signal-to-noise (SNR) improvement of approximately 10 dB and a typical introduced delay of approximately 8 samples. Such delay is well within the range of allowable delays in wire-line telephone systems. Computational complexity can be reduced in low-energy, long-time stationary noise environments by extracting and utilizing a set of fixed filters. In such case, the signal-to-noise improvement is typically on the order of 6-10 dB, with a good sound quality, and the introduced delay is again on the order of 8 samples. 
     Those skilled in the art will appreciate that the invention is not limited to the specific exemplary embodiments which have been described herein for purposes of illustration and that numerous alternative embodiments are also contemplated. For example, although the invention has been described in the context of hands-free telephony applications, those skilled in the art will appreciate that the teachings of the invention are equally applicable in any signal processing application in which it is desirable to suppress a particular signal component. The scope of the invention is therefore defined by the claims appended hereto, rather than the foregoing description, and all equivalents consistent with the meaning of the claims are intended to be embraced therein.