Patent Publication Number: US-7711556-B1

Title: Pseudo-cepstral adaptive short-term post-filters for speech coders

Description:
The present application is a continuation of U.S. patent application Ser. No. 10/684,852, filed 14 Oct. 2003, now U.S. Pat. No. 7,269,553 and claims the benefit of U.S. patent application Ser. No. 09/834,391 filed Apr. 13, 2001, now issued as U.S. Pat. No. 6,665,638, which claims the benefit of U.S. Provisional Patent Application No. 60/197,877 filed Apr. 17, 2000. The content of these patent applications is incorporated herein by reference including all references cited therein. 

   BACKGROUND OF THE INVENTION 
   1. Field of Invention 
   The invention relates to methods and systems that compensate for noise in digitized speech. 
   2. Description of Related Art 
   As telecommunications plays an increasingly important role in modern life, the need to provide clear and intelligible voice channels increases commensurately. However, providing clear, noise-free and intelligible voice channels has traditionally required high-bit-rate communication links, which can be expensive. While lowering the bit-rate of a voice channel can reduce costs, low-bit-rates tend to introduce side-effects, such as quantization noise, which can reduce the clarity and/or intelligibility of voice signals. Unfortunately, removing noise in a voice signal generated by low-bit-rate channels can require excessive processing power and distort the voice signal. Accordingly, there is a need for new technology to provide better voice channels that reduce processing power requirements while minimizing distortion. 
   SUMMARY OF THE INVENTION 
   The invention provides the short-term post-filtering methods and systems for digital voice communications. Generally, post-filtering improves the perceptual quality of the synthesized signal and is widely used in current low-bit-rate speech coders. The common post-filter consists of three filters: a long-term post-filter, a short-term post-filter and a tilt compensation filter. The long-term post filter generally relates to improving perceptual quality of speech by emphasizing pitch periodicity. The short-term post filter, adaptively constructed from LPC coefficients, removes perceptible noise from synthesized or reconstructed speech by de-emphasizing speech frequency components related to spectral valleys, or local minima. The tilt compensation filter is required to compensate for spectral tilt caused by the short-term post-filter. 
   In various exemplary embodiments, a set of linear predictive coding (LPC) coefficients is used to derive a second set of LPC coefficients having a reduced order, which can subsequently be used to derive a low-order short-term post-filter based on the pseudo-cepstrum. The low-order short-term post-filter can then adaptively remove perceptible noise from synthesized or reconstructed speech by emphasizing speech frequency components related to the formants of the LPC coefficients and de-emphasizing speech frequency components related to the spectral valleys of the LPC coefficients. The short-term post-filter can also compensate for spectral distortion such as spectral tilt and minimize phase distortion. 
   Other features and advantages of the present invention will be described below or will become apparent from the accompanying drawings and from the detailed description which follows. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is described in detail with regard to the following figures, wherein like numbers reference like elements, and wherein: 
       FIG. 1  is a representation of an exemplary human voice signal; 
       FIG. 2  is a representation of an exemplary logarithmic magnitude spectrum based on the human voice signal of  FIG. 1 ; 
       FIG. 3  is a is a representation of an exemplary LPC inverse transfer function based on the voice signal of  FIG. 1 ; 
       FIG. 4  is a representation of an exemplary residue signal based on the voice signal of  FIG. 1 ; 
       FIG. 5  is a representation of an exemplary logarithmic magnitude spectrum of the residual signal of  FIG. 4 ; 
       FIG. 6  is a block diagram of an exemplary communication system; 
       FIG. 7  is a block diagram of an exemplary embodiment of the post-filter of  FIG. 6 ; 
       FIG. 8  is a block diagram of an exemplary embodiment of the short-term filter of  FIG. 7 ; and 
       FIG. 9  is a flowchart outlining an exemplary operation of a process for filtering voice information. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   There is obviously an economic advantage in making telecommunication channels operate as inexpensively as possible. For digital communication channels such as modern long-distance phone lines and cellular phone links, there is a direct correlation to the cost of a voice communication channel and the number of bits per second the communicationchannel requires. 
   Traditionally, high-quality digital voice channels required high-bit-rates. However, by efficiently compressing a voice signal before transmission, bit-rates can be lowered without noticeable degradation of the clarity and/or intelligibility of the received voice signals. One efficient compression technique is the linear predictive coding (LPC) technique, which compresses human voices based on a model analogous to the human vocal system. That is, for a given time segment, or frame, of sampled speech, an LPC coding device will break the sampled speech into an excitation, or residue, portion that models the human larynx, and a corresponding LPC transfer function that models the human vocal tract. Fortunately, the quality of speech reconstruction can be dramatically improved while simultaneously reducing the processing complexity by modeling the vocal excitation signals with structured vector codebooks. This approach is typically referred to as the excited linear prediction (CELP) method, and it is the most common method of the current standard speech coders. 
   The general form of the LPC transfer function is shown in Eqs. (1) and (2): 
                       A   M     ⁡     (   z   )       =     1   +       ∑     i   =   1     M     ⁢           ⁢       a     M   .   i       ⁢     z     -   i               ;             ⁢             ⁢   or           (   1   )                 A   M ( z )=1 +a   M.1   z   −1   +a   M.2   z   −2   +a   M.3   z   −3    . . . a   M.M   z   −M   (2) 
   where a M.i  is the i-th LPC predictor coefficient, M is the order of the LPC transfer function, and (a M.1 , a M.2 , a M.3 , . . . a M.M ) are the LPC coefficients of the transfer function. 
     FIG. 1  shows an exemplary speech signal s(n)  10 . As shown in  FIG. 1 , an exemplary speech signal  10  is plotted against an amplitude axis  12  and along a time axis  14 .  FIG. 2  shows an exemplary logarithmic magnitude spectrum 20×log10|S(z)| of the speech signal s(n) of  FIG. 1 . The exemplary spectrum curve  20  is plotted against an amplitude axis  22  and along a frequency axis  24 . 
     FIG. 3  shows a graphic representation of an exemplary LPC inverse transfer function A- 1 ( z )  30  derived from the speech signal  10  of  FIG. 1 . As shown in  FIG. 3 , the inverse transfer function  30  is plotted against an amplitude axis  32  and along a frequency axis  34  and has three local maxima, or formants,  40 ,  42  and  44  and two local minima, or spectral valleys,  50  and  52 . The particular shape of the inverse transfer function  30  is related to the roots of transfer function A(z). That is, the formants are located coincident with the roots of A(z). The relationships between LPC transfer functions, their graphic representations and subsequent effects are well known and are described in Chen, J. and Gersho, A, “Adaptive Postfiltering for Quality Enhancement of Coded Speech”, IEEE Transactions on Speech and Audio Processing, Vol. 3, No. 1 (January 1995) incorporated herein by reference in its entirety. 
     FIG. 4  shows a representation of an LPC residue r(n)  60  of the speech signal s(n) of  FIG. 1  plotted against an amplitude axis  62  and along a time axis  64 . As discussed above, the residue  60  models the human larynx and compliments the LPC transfer function A(z) such that, when the signal residue  60  is passed through a filter having the inverse transfer function A- 1 ( z )  30 , a signal s′(n) will be synthesized, which will approximate the original speech signal s(n).  FIG. 5  shows an exemplary logarithmic magnitude spectrum 20×log10|R(z)| of the residual signal r(n)  70  of  FIG. 4 . 
   The exemplary residual spectrum curve  70  is plotted against an amplitude axis  72  and along a frequency axis  74 . As discussed above, the bit-rates of communication channels can be lowered with little noise and/or distortion by applying an LPC compression technique to a speech signal, passing the LPC coefficients and residue to a receiver, and reconstructing/synthesizing the speech signal at a receiver. However, there is a practical limit to LPC compression; and as bit-rates for LPC channels further drop, quantization noise and other distortions become increasingly noticeable until the received voice signal becomes unacceptable. 
   To remove the resulting deleterious noise, a post-filtering step can be added to the synthesized speech process. Because of the nature of human perception, it can be desirable that such a post-filtering step selectively enhance the frequency regions near the formants and selectively attenuate the frequency regions near the spectral valley regions of a given LPC inverse transfer function A- 1 ( z ). Furthermore, because the formants and spectral valleys can vary over time, it becomes advantageous to adaptively vary the post-filtering step to accommodate the varying formants and spectral valleys of A- 1 ( z ). 
   Unfortunately, conventional domains relating to linear predictive coding (LPC) coefficients, log area ratio (LAR) coefficients, line spectrum frequency (LSF) coefficients as well as any other known coefficients are not well-suited to creating post-filters. However, by mapping LPC parameters into the pseudo-cepstrum, a domain conceptually located between the LPC and LSF domains, a set of pseudo-cepstral coefficients is produced that can more efficiently and effectively form adaptive post-filters capable of removing perceptible noise with minimal distortion. One advantage of using the pseudo-cepstrum is that low-order filters can be easily produced that can perform as well as filters requiring twice as many coefficients. Still another advantage to using the pseudo-cepstrum is that spectral correction techniques such tilt-filters generally present in other post-filters can be eliminated. 
     FIG. 6  shows an exemplary block diagram of a communication system  100 . The system  100  includes a transmitter  110 , a communication channel  130  and a receiver  140 . The transmitter  110  has a data source  120  and a linear predictive coding (LPC) analyzer  124 , and the receiver  140  has a LPC synthesizer  150 , a post-filter  160  and a data sink  170 . The receiver  110  provides voice information r(n) to the communication channel  130  that, in turn, provides the channeled voice information {circumflex over (r)}(n) to the receiver  140 . 
   In operation, the data source  120  provides voice signals s(n) to the LPC analyzer  124  via link  122 . In various exemplary embodiments, the data source  120  can be any one of a number of different types of sources such as a person speaking into a microphone, a computer generating synthesized speech, a storage device such as magnetic tape, a disk drive, an optical medium such as a compact disk, or any known or later developed combination of software and hardware of capable of generating, relaying or recalling from storage any information capable of being transmitted to the LPC analyzer. It should be further appreciated that the speech signals can be any form of speech, such as speech produced by a human, mechanical speech or information representing speech produced by a speech synthesizer or any other form of signal or information that can represent speech. However, for the purpose of discussion below, the data source  120  will be assumed to be a person speaking into the receiver of a cellular telephone. 
   As the LPC analyzer  124  receives speech signals from the data source  120  via link  122 , it divides the speech signals into individual time frames. For example, the LPC analyzer  124  can receive a continuous speech signal and divide the continuous speech into contiguous frames of 20 ms each. The LPC analyzer  124  can then perform an LPC analysis on each speech frame to generate LPC coefficients and residue information pertaining to each frame that can be exported to the communication channel  130  via link  126 . The exemplary LPC analyzer  124  is a dedicated signal processor with an analog-to-digital converter and other peripheral hardware. However, the LPC analyzer  124  can alternatively be a digital signal processor or micro-controller with various peripheral hardware, a custom application specific integrated circuit (ASIC), discrete electronic circuits or any other known or later developed device capable of receiving voice signals from the data source  120  and providing LPC coefficients and residue information to the communication channel  130 . 
   Unfortunately, the LPC coefficients (aM. 1 , aM. 2 , aM. 3 , . . . aM.M) cannot be quantized directly due to stability problems. Instead, the LPC coefficients first must be converted to another form of information. For example, a set of LPC coefficients can be converted to a set of reflection coefficients, log area ratio (LAR) coefficients, line spectrum frequency (LSF) coefficients or coefficients of some other domain, and converted into the LPC coefficients in the decoder. The communication channel  130  receives the quantized LPC coefficients (aM. 1 , aM. 2 , aM. 3 , . . . aM.M) and residue information r(n) via link  126  and provides the channeled LPC coefficients (âM. 1 , âM. 2 , âM. 3 , . . . âM.M) and channeled residue information {circumflex over (r)}(n) to the receiver  140  via link  136 . 
   Generally, it should be appreciated that the residue information r(n) and the channeled residue information {circumflex over (r)}(n) should ideally be identical. However, when a channel error occurs, the residue information r(n) and the channeled residue information {circumflex over (r)}(n) can vary in the absence of error correction. However, it should be assumed for the purpose of the following embodiments that the residue information r(n) and the channeled residue information are identical. 
   The exemplary communication channel  130  is a wireless link over a cellular telephone network. However, the communication channel  130  can alternatively be a hardwired link such as a telephony T1 or E1 line, an optical link, other wireless/radio links, a sonic link, or any other known or later developed communications device or system capable of receiving LPC coefficients and residue information from the transmitter  110  and providing this data to the receiver  140 . 
   The LPC synthesizer  150  receives LPC coefficients and residue information for various speech frames from the communication channel  130  via link  136 . As speech frames are received, the LPC synthesizer  150  constructs a filter/process Â- 1 ( z ) using the LPC coefficients for each frame. The LPC synthesizer  150  then processes the respective residue using the filter to synthesize a speech signal s′(n), which is an approximation of the original speech s(n), and provides each frame of synthesized speech to the post-filter  160  via link  152 . 
   The exemplary LPC synthesizer  150  is a dedicated signal processor with peripheral hardware. However, the LPC synthesizer  150  can be any device capable of receiving LPC coefficients and residue information from a communication channel and providing synthesized speech to a post-filter, such as a digital signal processor or micro-controller with various peripheral hardware, a custom application specific integrated circuit (ASIC), discrete electronic circuits and the like. 
   The post-filter  160  can receive synthesized speech frames from the LPC synthesizer  150  via link  152  and can further receive LPC coefficients either from the LPC synthesizer  150 , directly from the communication channel  130  or from any other conduit capable of providing LPC coefficients. The post-filter  160  then constructs or modifies various internal filters, processes and coefficients within the post-filter  160 , filters the synthesized speech frames and provides the filtered speech frames s′(n) to the data sink  170 . 
   The exemplary post-filter  160  is a dedicated signal processor with peripheral hardware including a digital-to-analog converter. However, the post-filter  160  can be any device capable of receiving LPC coefficients and synthesized speech, constructing or modifying various filters, process and coefficients, filtering the synthesized speech using the various filters, processes and coefficients and providing filtered speech to the data sink  170 , such as a digital signal processor or micro-controller with various peripheral hardware, a custom application specific integrated circuit (ASIC), discrete electronic circuits and the like. 
   The data sink  170  receives data from the post-filter  160  via link  162 . The exemplary data sink  170  is an electronic circuit having an analog-to-digital converter, an amplifier and microphone capable of transforming electronic signals into mechanical/acoustical signals. However, the data sink  170  alternatively can be any combination of hardware and software capable of receiving speech data, such as a transponder, a computer with a storage system or any other known or later developed device or system capable of receiving, relaying, storing, sensing or perceiving signals provided by the post-filter  160 . 
     FIG. 7  is a block diagram of an exemplary post-filter  140  that can receive synthesized speech data, LPC coefficients and residue information via link  152  and provide filtered speech data to link  162 . As shown in  FIG. 7 , the exemplary post-filter has a long-term filter HL(z)  410 , a short-term filter HS(z)  420 , an automatic gain control (AGC)  430  and a gain estimator  440 . The long-term filter  410  receives frames of synthesized speech, performs a first filtering operation on the frames of synthesized speech, then passes the filtered speech to short-term filter  420 , which can perform a second filtering operation. The short-term filter  420  can then pass its filtered speech data to the AGC  430 , which scales the filtered speech to correct for gain mismatch caused by the filters  410  and  420 . After the AGC  430  compensates for gain error, the AGC can provide the scaled speech data to link  162 . 
   In operation, the long-term filter  410  receives frames of synthesized speech and respective residue information and subsequently filters the speech frames using the residual information. Generally, the residue information can be used to compute the pitch delay and gain of the long-term filter  410  such that the long-term filter  410  can improve the perceptual quality of the synthesized speech by emphasizing pitch periodicity, especially for voiced frames. The processes and functions of long-term filters are well known in the art and are described in Chen, J. and Gersho, A, “Adaptive Postfiltering for Quality Enhancement of Coded Speech”, IEEE Transactions on Speech and Audio Processing, Vol. 3, No. 1, pp. 63-66 (January 1995). After the long-term filter  410  performs its filtering processes, it provides the filtered data to the short-term filter  420  via link  412 . 
   The exemplary long-term filter  410  is implemented using a digital signal processor operating dedicated firmware and having various peripheral devices to accommodate input/output functions. However, the long-term filter  410  can alternatively be implemented using a digital signal processor, a micro-controller, an ASIC or other specialized electronic hardware or any other known or later developed device that can receive frames of speech data, perform long-term filtering operations such as emphasizing pitch periodicity, and provide the filtered data to the short-term filter  420 . 
   The short-term filter  420  receives frames of filtered synthesized speech data from the long-term filter  410  and further receives the LPC coefficients either from the long-term filter  410 , directly from the communication channel  120  via link  152 , or from some other link capable of providing LPC coefficients. 
   In operation, the short-term filter  420  can perform a filtering operation based on the LPC coefficients to improve the perceptual quality of the synthesized speech. Referring to the LPC inverse transfer function  30  of  FIG. 3 , it should be appreciated that the human ear is particularly sensitive to noise in the spectral valley regions  50  and  52 , but relatively insensitive to noise at the formants  40 ,  42  and  44 . Accordingly, for any transfer function having formants and spectral valleys, it can be desirable to emphasize frequencies at or near the formants while de-emphasizing frequencies at or near the spectral valleys. 
   As discussed above, synthesizing short-term filters using conventional techniques can cause spectral distortions that can require a spectral correction filter such as a tilt filter. However, by mapping LPC coefficients to the pseudo-cepstrum, a domain between the LPC and the LSF domains, stable short-term post-filters can be easily synthesized that do not require an additional tilt filter. 
   Conversion from the LPC domain to the pseudo-cepstrum can start by defining two polynomials, the symmetric polynomial of Eq. (3) and the anti-symmetric polynomial of Eq. (4): 
                     P   M     ⁡     (   z   )       =           A   M     ⁡     (   z   )       +       z     -     (     M   +   1     )         ⁢       A   M     ⁡     (     z     -   1       )           =       ∑     k   =   0       M   +   1       ⁢           ⁢       p     M   .   k       ⁢     z     -   k                     (   3   )                   Q   M     ⁡     (   z   )       =           A   M     ⁡     (   z   )       -       z     -     (     M   +   1     )         ⁢       A   M     ⁡     (     z     -   1       )           =       ∑     k   =   0       M   +   1       ⁢           ⁢       q     M   .   k       ⁢     z     -   k                     (   4   )               
where A M (z)=1+a M.1 z −1 +a M.2 z −2 a M.3 z −3  . . . a M.M z −m  from Eq. (2) above, a i  is the i-th LPC coefficient and the coefficients p 0 =q 0 =1. Transforming to pseudo-cepstrum is then defined by Eq. (5):
 
   
     
       
         
           
             
               
                 
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   Given the relationship between LPC coefficients, a M.i , and LPC cepstral coefficients, c M.i , is defined by: 
                   log   ⁡     (       A   M     ⁡     (   z   )       )       =     -       ∑     n   =   1     ∞     ⁢           ⁢       c     M   .   n       ⁢     z     -   n                     (   6   )               
the cepstral difference C D (z) between cepstral coefficients, c M.n , and the pseudo-cepstral coefficients, c′ M.n , can be written as:
 
                       C   D     ⁡     (   z   )       =     -       ∑     n   =   1     ∞     ⁢           ⁢       (       c     M   .   n       -       (     c   M   ′     )       .   n         )     ⁢     z     -   n               ;           ⁢   or           (   7   )                 C   D ( z )=½log( P   M ( z ) Q   M ( z ))−log( A   M ( z )); or  (8)   C   D ( z )=½log(1− R   2   M ( z ))  (9) 
where R M (z)=(z −(M+1) A M (z −1 ))/A M (z). Details of the pseudo-cepstrum and transformation from the LPC domain can be found in at least Kim, H., Choi, S. and Lee, H., “On Approximating Line Spectral Frequencies to LPC Cepstral Coefficients”,  IEEE Transactions on Speech and Audio Processing , Vol. 8, No. 2, pp. 195-199, (March 2000) herein incorporated by reference in its entirety.
 
   From Eqs. (7)-(9), 1−R 2   M (z) can be rewritten as Eq. (10):
 
1 −R   2   M ( z )=( P   M ( z ) Q   M ( z ))/ A   2   M ( z )  (10)
 
where R 2   M (z)=1 when z=±1 and exp (jω M.i ) for i=1, 2, . . . M, where ω M.i  is the i-th LSF coefficient of order M. If the roots of P M (z), Q M (z) and A 2   M (z) are inside the unit circle, a generalized short-term post-filter can be realized having the form:
 
 H   S ( z )=( P   M ( z/α   1 ) Q   M ( z/α   2 ))/ A   2   M ( z/β )  (11)
 
where α 1 , α 2 , and β are control parameters and 0&lt;α 1 , 0&lt;α 2 , and β&lt;1, or
 
 H   S ( z )≅( P   M ( z/α   1 ) Q   M ( z/α   2 ))/ A   M ( z/ 2β)  (12)
 
when 0&lt;α 1 , 0&lt;α 2 , and β&lt;0.5.
 
   A first benefit of short-term post-filters based on Eq. (12) is that they automatically compensate for spectral tilt and do not require tilt-filters. Another benefit of short-term post-filters based on Eq. (12) is that they will produce negligible phase distortion of speech signals if the values of the control parameters α l , α 2 , and β are selected such that α 1 +α 2 =2β. 
   The values of control parameters α 1 , α 2 , and β can be determined experimentally or can be set according to the communication environment. Generally, the values of the control parameters will vary with the bit-rate of a communication system, the type of speech coder used, or a function of other factors such as effects of various noise sources. For example, for a high-bit-rate communication system with low quantization noise, a weak post-filter will provide optimal performance, i.e., a low value of β is preferable. However, as the bit-rate drops or other noise sources increase, β will increase commensurately. 
   While short-term post-filters can be synthesized according to Eq. (12), it can be advantageous to synthesize short-term post-filters having reduced order. For example, for an LPC transfer function of order ten, a short-term pseudo-cepstral filter of order ten can be synthesized or alternatively short-term pseudo-cepstral filters having orders less than ten can also be synthesized according to Eq. (13):
 
 H   m   S ( z )≅( P   m ( z/α   1 ) Q   m ( z/α   2 ))/ A   M ( z/ 2β)  (13)
 
where 1≦m≦M, M is the order of the LPC transfer function and m is the desired order of the synthesized short-term filter and where P m (z/α i ) and Q m (z/α 2 ) can be defined by Eqs (14) and (15):
 
 P   m ( z )= A   m ( z )+ z   −(m+1)   A   m ( z   −1 ); and  (14)
 
 Q   m ( z )= A   m ( z )− z   −m+1)   A   m ( z   −1 ).  (15)
 
   The LPC coefficients of order m can be recursively generated through a step-down process described by Eq. (16):
 
 a   l-i.i =( a   l.i   −k   l   a   l.l-i )/(1− k   2   l )  (16)
 
where l=M, M−1, . . . m+1; i=1, 2 . . . l−1; k l =a 1.1  and a l-1.0 =1. Details of the step-down procedure can be found in at least Markel, J. and Gray, A.,  Linear Prediction of Speech pp.  95-97 (New York: Springer-Verlag 1976) herein incorporated by reference in its entirety. It should be appreciated that, as m decreases to lower orders, spectral tilt of the LPC transfer function can increase. However, because of the nature of the pseudo-cepstrum, short-term filters generated according to Eqs. (13)-(16) will not require tilt filters or other equivalent spectral correction.
 
   The exemplary short-term filter  420  is implemented using a digital signal processor operating dedicated firmware and having various peripheral devices to accommodate input/output functions. However, the short-term filter  420  can alternatively be implemented using a digital signal processor, a micro-controller, an ASIC or other specialized electronic hardware or any other known or later developed device that can receive frames of speech data, filter the speech data to emphasis and de-emphasis different spectral frequencies based on an LPC inverse transfer function and provide the filtered data to the AGC  430 . 
   The AGC  430  receives the filtered speech via link  422  and scales the filtered speech to correct for gain errors caused by the filters  410  and  420 . For example, given a frame of synthesized speech having an overall power level of ten decibels, if the filtered speech produced by the filters  410  and  420  has a power level of six decibels, the AGC  430  will increase the level of the filtered data by four decibels. 
   In operation, the ACG  430  adjusts its gain level based on information provided by the gain estimator  440  via link  442  and provides the scaled speech to the link  162 . In various exemplary embodiments, the gain estimator  440  determines the gain mismatch produced by the filters  410  and  420  by measuring the power of each frame of synthesized speech at the link  152 , measuring the power of each frame of filtered speech at the link  422  and taking the difference of the power levels. 
     FIG. 8  is a block diagram of an exemplary short-term filter  420 . The short-term filter  420  has a controller  510 , a memory  520 , filter generating circuits  530 , scaling circuits  540 , filtering circuits  550 , an input interface  580  and output interface  590 . The various components  510 - 590  are linked together via control/data bus  502 . The links  422  and  162  are connected to the input-interface  580  and output-interface  590 , respectively. 
   As frames of synthesized speech and respective LPC coefficients are presented to the input interface  580 , the controller  510  can transfer the synthesized speech and respective LPC coefficients to the memory  520 . The memory  520  can store the synthesized speech and respective LPC coefficients and other data generated by the short-term filter  420  during speech processing. 
   In various exemplary embodiments, the filter generating circuits  530 , under control of the controller  510 , can receive the LPC coefficients and determine the pseudo-cepstral coefficients for a short-term filter based on Eq. (12) above to synthesize a short-term filter of the same order as that of the LPC transfer function described by the LPC coefficients. 
   In other various exemplary embodiments, the filter generating circuits  530  can determine the pseudo-cepstral coefficients for a short-term filter based on Eq. (13)-(16) above to synthesize a short-term filter having a lower order than that of the LPC transfer function. For example, given an LPC transfer function of order ten, i.e., A 10 ( z )=1+a 10 . 1  z−1+a 10 . 2  z−2+a 10 . 3  z−3 . . . a 10 . 10  z−10, Eq. (16) can be used to reduce the order to six, i.e., A 6 ( z )=1+a 6 . 1  z−1+a 6 . 2  z−2+a 6 . 3  z−3 . . . a 6 . 6  z−6. Subsequently, P 6 ( z ) and Q 6 ( z ) can be determined using Eqs. (14) and (15), and H 6 S(z) can then be calculated using Eq. (13). Once the desired short-term filter coefficients are synthesized, the filter generating circuits  530 , under control of the controller  510 , can transfer the filter coefficients to the scaling circuits  540 . 
   The scaling circuits  540  can receive the short-term filter coefficients, determine the values of control parameters α 1 , α 2 , and β of either Eqs. (12) or (13), scale the short-term filter coefficients accordingly and provide the scaled filter coefficients to the filtering circuits  550 . As discussed above, control parameters α 1 , α 2 , and β can be determined experimentally or can be set based on various aspects of a communication environment, such as the system bit-rate, the type of speech coder used, or based on other factors such as effects of various noise sources. While control parameters α 1 , α 2 , and β can be adjusted independently, as discussed above, short-term post-filters synthesized using Eqs. (12) or (13) will produce negligible phase distortion if the values of control parameters α 1 , α 2 , and β are selected such that α 1 +α 2 =2β. Once the filter coefficients of the short-term filter are scaled, the scaling circuits  540 , under control of the controller  510 , transfer the scaled short-term filter to the filtering circuits  550 . 
   The filtering circuits  550 , under control of the controller  510 , can receive the frame of speech stored in the memory  520  and subsequently filter the speech data in each frame. As each frame of speech data is filtered, the filtering circuits  550 , under control of the controller  510 , can export the filtered speech to the link  162  through the output interface  590 . 
     FIG. 9  is a flowchart outlining an exemplary method for adaptively forming short-term filters and filtering speech data using the short-term filters. The operation starts in step  710  where the control parameters α 1 , α 2 , and β are determined. As discussed above, control parameters α 1 , α 2 , and β can be determined independently, but short-term post-filters will produce negligible phase distortion if the values of control parameters α 1 , α 2 , and β are selected such that α 1 +α 2 =2β. Next, in step  720 , the LPC coefficients for a frame of speech are received. Control continues to step  730 . 
   In step  730 , a determination is made whether to reduce the order of the LPC transfer function described by the LPC coefficients received in step  720 . If the order of the LPC transfer function is to be reduced, control continues to step  740 ; otherwise control jumps to step  750 . In step  740 , the order of the LPC transfer function is reduced using Eq. (16) above to generate a reduced set of LPC coefficients and control continues to step  750 . 
   In step  750 , the pseudo-cepstral coefficients for a short-term filter are generated. In various exemplary embodiments, the pseudo-cepstral coefficients are generated using the LPC coefficients received in step  720  and Eq. (12) above. In other various exemplary embodiments, the pseudo-cepstral coefficients are generated using the reduced set of LPC coefficients generated in step  740  and Eq. (13) above. Once the pseudo-cepstral coefficients are generated, control continues to step  760 . 
   In step  760 , a frame of speech related to the LPC coefficients of step  720  is received. Next, in step  770 , a short-term filtering operation is performed on the received frame of speech using the filter coefficients generated in step  750 . Control continues to step  780 . 
   In step  780 , a long-term filtering operation is performed to improve the perceptual quality of the synthesized speech by emphasizing pitch periodicity. Next, in step  790 , a gain control operation is performed to adjust for gain mismatch produced by the filtering steps of  760  and  770 . Then, in step  800 , the filtered and scaled speech data produced in steps  720 - 780  is provided to a data sink such as a speaker, a storage device and the like. Control continues to step  810 . 
   In step  810 , a determination is made as to whether any more frames of speech data are to be filtered and scaled. If there are more speech frames to be filtered, control jumps back to step  720  where the next frame of LPC coefficients is received. Otherwise, control continues to step  820  where the process stops. 
   In the exemplary embodiment shown in  FIG. 6 , the transmitter  110  and receiver  140  are implemented using programmed digital signal processors equipped with a peripheral devices. However, the transmitter  110  and receiver  140  can also be implemented on a general or special purpose computer, a programmed microprocessor or micro-controller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwire electronic or logic circuit such as discrete element circuit, a programmable logic device such as PLD, PLA, FPGA or PAL, or the like. In general, any device capable of implementing a finite state machine that is in turn capable of implementing the communication system  100  of  FIG. 6 , any of the devices of  FIGS. 7 and 8 , or the flowchart of  FIG. 9  can be used to implement the transmitter  110  and/or receiver  140 . 
   It should be similarly understood that each of the components and circuits shown in  FIGS. 6-8  can be implemented as distinct optical devices. Alternatively, each of the optical components and circuits shown in  FIGS. 6-8  can be implemented as physically indistinct or shared hardware or combined with other components and circuits otherwise not related to the devices of  FIGS. 6-8  and the flowchart of  FIG. 9 . The particular form each optical component and circuit shown in  FIGS. 6-8  will take is a design choice and will be obvious and predictable to those skilled in the art. 
   While this invention has been described in conjunction with the specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art. Accordingly, preferred embodiments of the invention as set forth herein are intended to be illustrative and not limiting. Thus, there are changes that may be made without departing from the spirit and scope of the invention.