Abstract:
A method and system are provided for synthesizing a corrupted frame output from a decoder including one or more predictive filters. The corrupted frame is representative of one segment of a decoded signal output from the decoder. The method comprises extrapolating a replacement frame based upon another segment of the decoded signal and substituting the replacement frame for the corrupted frame. Finally, the internal states of the filters are updated based upon the substituting.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit of U.S. Provisional Application No. 60/312,789, filed Aug. 17, 2001, entitled “Frame Erasure Concealment for Predictive Speech Coding Based On Extrapolation of Speech Waveform,” and U.S. Provisional Application No. 60/344,374, filed Jan. 4, 2002, entitled “Frame Erasure Concealment for Predictive Speech Coding Based On Extrapolation of Speech Waveform,” both of which are incorporated by reference herein in their entireties. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to digital communications. More particularly, the present invention relates to the enhancement of speech quality when frames of a compressed bit stream representing a speech signal are lost within the context of a digital communications system. 
   2. Related Art 
   In speech coding, sometimes called voice compression, a coder encodes an input speech or audio signal into a digital bit stream for transmission. A decoder decodes the bit stream into an output speech signal. The combination of the coder and the decoder is called a codec. The transmitted bit stream is usually partitioned into frames. In wireless or packet networks, sometimes frames of transmitted bits are lost, erased, or corrupted. This condition is called frame erasure in wireless communications. The same condition of erased frames can happen in packet networks due to packet loss. When frame erasure happens, the decoder cannot perform normal decoding operations since there are no bits to decode in the lost frame. During erased frames, the decoder needs to perform frame erasure concealment (FEC) operations to try to conceal the quality-degrading effects of the frame erasure. 
   One of the earliest FEC techniques is waveform substitution based on pattern matching, as proposed by Goodman, et al. in “Waveform Substitution Techniques for Recovering Missing Speech Segments in Packet Voice Communications”,  IEEE Transaction on Acoustics, Speech and Signal Processing , December 1986, pp. 1440-1448. This scheme was applied to Pulse Code Modulation (PCM) speech codec that performs sample-by-sample instantaneous quantization of speech waveform directly. This FEC scheme uses a piece of decoded speech waveform immediately before the lost frame as the template, and slides this template back in time to find a suitable piece of decoded speech waveform that maximizes some sort of waveform similarity measure (or minimizes a waveform difference measure). 
   Goodman&#39;s FEC scheme then uses the section of waveform immediately following a best-matching waveform segment as the substitute waveform for the lost frame. To eliminate discontinuities at frame boundaries, the scheme also uses a raised cosine window to perform an overlap-add technique between the correctly decoded waveform and the substitute waveform. This overlap-add technique increases the coding delay. The delay occurs because at the end of each frame, there are many speech samples that need to be overlap-added to obtain the final values, and thus cannot be played out until the next frame of speech is decoded. 
   Based on the work of Goodman above, David Kapilow developed a more sophisticated version of an FEC scheme for G.711 PCM codec. This FEC scheme is described in Appendix I of the ITU-T Recommendation G.711. However, both the FEC of Goodman and the FEC scheme of Kapilow are limited to PCM codecs with instantaneous quantization. 
   For speech coding, the most popular type of speech codec is based on predictive coding. Perhaps the first publicized FEC scheme for a predictive codec is a “bad frame masking” scheme in the original TIA IS-54 VSELP standard for North American digital cellular radio (rescinded in September 1996). Here, upon detection of a bad frame, the scheme repeats the linear prediction parameters of the last frame. This scheme derives the speech energy parameter for the current frame by either repeating or attenuating the speech energy parameter of last frame, depending on how many consecutive bad frames have been counted. For the excitation signal (or quantized prediction residual), this scheme does not perform any special operation. It merely decodes the excitation bits, even though they might contain a large number of bit errors. 
   The first FEC scheme for a predictive codec that performs waveform substitution in the excitation domain is probably the FEC system developed by Chen for the ITU-T Recommendation G.728 Low-Delay Code Excited Linear Predictor (CELP) codec, as described in U.S. Pat. No. 5,615,298 issued to Chen, titled “Excitation Signal Synthesis During Frame Erasure or Packet Loss.” In this approach, during erased frames, the speech excitation signal is extrapolated depending on whether the last frame is a voiced or an unvoiced frame. If it is voiced, the excitation signal is extrapolated by periodic repetition. If it is unvoiced, the excitation signal is extrapolated by randomly repeating small segments of speech waveform in the previous frame, while ensuring the average speech power is roughly maintained. 
   What is needed therefore is an FEC technique that avoids the noted deficiencies associated with the conventional decoders. For example, what is needed is an FEC technique that avoids the increased delay created in the overlap-add operation of Goodman&#39;s approach. What is also needed is an FEC technique that can ensure the smooth reproduction of a speech or audio waveform when the next good frame is received. 
   SUMMARY OF THE INVENTION 
   Consistent with the principles of the present invention as embodied and broadly described herein, an exemplary FEC technique includes a method of synthesizing a corrupted frame output from a decoder including one or more predictive filters. The corrupted frame is representative of one segment of a decoded signal output from the decoder. The method comprises extrapolating a replacement frame based upon another segment of the decoded signal, substituting the replacement frame for the corrupted frame, and updating internal states of the filters based upon the substituting. 
   Further embodiments, features, and advantages of the present invention, as well as the structure and operation of the various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention and, together with the description, explain the purpose, advantages, and principles of the invention. In the drawings: 
       FIG. 1  is a block diagram illustration of a conventional predictive decoder; 
       FIG. 2  is a block diagram illustration of an exemplary decoder constructed and arranged in accordance with the present invention; 
       FIG. 3(   a ) is a plot of an exemplary unnormalized waveform attenuation window functioning in accordance with the present invention; 
       FIG. 3(   b ) is a plot of an exemplary normalized waveform attenuation window functioning in accordance with the present invention; 
       FIG. 4(   a ) is a flowchart illustrating an exemplary method of performing frame erasure concealment in accordance with the present invention; 
       FIG. 4(   b ) is a continuation of the flowchart shown in  FIG. 4(   a ); and 
       FIG. 5  is a block diagram of an exemplary computer system on which the present invention can be practiced. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The following detailed description of the present invention refers to the accompanying drawings that illustrate exemplary embodiments consistent with this invention. Other embodiments are possible, and modifications may be made to the embodiments within the spirit and scope of the present invention. Therefore, the following detailed description is not meant to limit the invention. Rather, the scope of the invention is defined by the appended claims. 
   It would be apparent to one of skill in the art that the present invention, as described below, may be implemented in many different embodiments of hardware, software, firmware, and/or the entities illustrated in the drawings. Any actual software code with specialized control hardware to implement the present invention is not limiting of the present invention. Thus, the operation and behavior of the present invention will be described with the understanding that modifications and variations of the embodiments are possible, given the level of detail presented herein. Before describing the invention in detail, it is helpful to describe an exemplary environment in which the invention may be implemented. 
   The present invention is particularly useful in the environment of the decoder of a predictive speech codec to conceal the quality-degrading effects of frame erasure or packet loss.  FIG. 1  illustrates such an environment. The general principles of the invention can be used in any linear predictive codec, although the preferred embodiment described later is particularly well suited for a specific type of predictive decoder. 
   The present invention is an FEC technique designed for predictive coding of speech. One characteristic that distinguishes it from the techniques mentioned above, is that it performs waveform substitution in the speech domain rather than the excitation domain. It also performs special operations to update the internal states, or memories, of predictors and filters inside the predictive decoder to ensure maximally smooth reproduction of speech waveform when the next good frame is received. 
   The present invention also avoids the additional delay associated with the overlap-add operation in Goodman&#39;s approach and in ITU-T G.711 Appendix I. This is achieved by performing overlap-add between extrapolated speech waveform and the ringing, or zero-input response of the synthesis filter. Other features include a special algorithm to minimize buzzing sounds during waveform extrapolation, and an efficient method to implement a linearly decreasing waveform envelope during extended frame erasure. Finally, the associated memories within the log-gain predictor are updated. 
   As stated above, the present invention is not restricted to a particular speech codec. Instead, it&#39;s generally applicable to predictive speech codecs, including, but not limited to, Adaptive Predictive Coding (APC), Multi-Pulse Linear Predictive Coding (MPLPC), CELP, and Noise Feedback Coding (NFC), etc. 
   Before discussing the principles of the invention, a description of a conventional decoder of a standard predictive codec is needed.  FIG. 1  is a block diagram illustration of a conventional predictive decoder  100 . The decoder  100  shown in  FIG. 1  can be used to describe the decoders of APC, MPLPC, CELP, and NFC speech codecs. The more sophisticated versions of the codecs associated with predictive decoders typically use a short-term predictor to exploit the redundancy among adjacent speech samples and a long-term predictor to exploit the redundancy between distant samples due to pitch periodicity of, for example, voiced speech. 
   The main information transmitted by these codecs is the quantized version of the prediction residual signal after short-term and long-term prediction. This quantized residual signal is often called the excitation signal because it is used in the decoder to excite the long-term and short-term synthesis filter to produce the output decoded speech. In addition to the excitation signal, several other speech parameters are also transmitted as side information frame-by-frame or subframe-by-subframe. 
   An exemplary range of lengths for each frame (called frame size) can be 5 ms to 40 ms, with 10 ms and 20 ms as the two most popular frame sizes for speech codecs. Each frame usually contains a few equal-length subframes. The side information of these predictive codecs typically includes spectral envelope information in the form of the short-term predictor parameters, pitch period, pitch predictor taps (both long-term predictor parameters), and excitation gain. 
   In  FIG. 1 , the conventional decoder  100  includes a bit de-multiplexer  105 . The de-multiplexer  105  separates the bits in each received frame of bits into codes for the excitation signal and codes for short-term predictor, long-term predictor, and the excitation gain. 
   The short-term predictor parameters, often referred to as the linear predictive coding (LPC) parameters, are usually transmitted once a frame. There are many alternative parameter sets that can be used to represent the same spectral envelope information. The most popular of these is the line-spectrum pair (LSP) parameters, sometimes called line-spectrum frequency (LSF) parameters. In  FIG. 1 , LSPI represents the transmitted quantizer codebook index representing the LSP parameters in each frame. A short-term predictive parameter decoder  110  decodes LSPI into an LSP parameter set and then converts the LSP parameters to the coefficients for the short-term predictor. These short-term predictor coefficients are then used to control the coefficient update of a short-term predictor  120 . 
   Pitch period is defined as the time period at which a voiced speech waveform appears to be repeating itself periodically at a given moment. It is usually measured in terms of a number of samples, is transmitted once a subframe, and is used as the bulk delay in long-term predictors. Pitch taps are the coefficients of the long-term predictor. The bit de-multiplexer  105  also separates out the pitch period index (PPI) and the pitch predictor tap index (PPTI), from the received bit stream. A long-term predictive parameter decoder  130  decodes PPI into the pitch period, and decodes the PPTI into the pitch predictor taps. The decoded pitch period and pitch predictor taps are then used to control the parameter update of a generalized long-term predictor  140 . 
   In its simplest form, the long-term predictor  140  is just a finite impulse response (FIR) filter, typically first order or third order, with a bulk delay equal to the pitch period. However, in some variations of CELP and MPLPC codecs, the long-term predictor  140  has been generalized to an adaptive codebook, with the only difference being that when the pitch period is smaller than the subframe, some periodic repetition operations are performed. The generalized long-term predictor  140  can represent either a straightforward FIR filter, or an adaptive codebook, thus covering most of the predictive speech codecs presently in use. 
   The bit de-multiplexer  105  also separates out a gain index GI and an excitation index CI from the input bit stream. An excitation decoder  150  decodes the CI into an unscaled excitation signal, and also decodes the GI into the excitation gain. Then, it uses the excitation gain to scale the unscaled excitation signal to derive a scaled excitation gain signal uq(n), which can be considered a quantized version of the long-term prediction residual. An adder  160  combines the output of the generalized long-term predictor  140  with the scaled excitation gain signal uq(n) to obtain a quantized version of a short-term prediction residual signal dq(n). An adder  170  combines the output of the short-term predictor  120  to dq(n) to obtain an output decoded speech signal sq(n). 
   A feedback loop is formed by the generalized long-term predictor  140  and the adder  160  and can be regarded as a single filter, called a long-term synthesis filter  180 . Similarly, another feedback loop is formed by the short term predictor  120  and the adder  170 . This other feedback loop can be considered a single filter called a short-term synthesis filter  190 . The long-term synthesis filter  180  and the short-term synthesis filter  190  combine to form a synthesis filter module  195 . 
   In summary, the conventional predictive decoder  100  depicted in  FIG. 1  decodes the parameters of the short-term predictor  120  and the long-term predictor  140 , the excitation gain, and the unsealed excitation signal. It then scales the unscaled excitation signal with the excitation gain, and passes the resulting scaled excitation signal uq(n) through the long-term synthesis filter  180  and the short-term synthesis filter  190  to derive the output decoded speech signal sq(n). 
   When a frame of input bits is erased due to fading in a wireless transmission or due to packet loss in packet networks, the decoder  100  in  FIG. 1  unfortunately looses the indices LSPI, PPI, PPTI, GI, and CI, needed to decode the speech waveform in the current frame. 
   According to the principles of the present invention, the decoded speech waveform immediately before the current frame is stored and analyzed. A waveform-matching search, similar to the approach of Goodman is performed, and the time lag and scaling factor for repeating the previously decoded speech waveform in the current frame are identified. 
   Next, to avoid the occasional buzz sounds due to repeating a waveform at a small time lag when the speech is not highly periodic, the time lag and scaling factor are sometimes modified as follows. If the analysis indicates that the stored previous waveform is not likely to be a segment of highly periodic voiced speech, and if the time lag for waveform repetition is smaller than a predetermined threshold, another search is performed for a suitable time lag greater than the predetermined threshold. The scaling factor is also updated accordingly. 
   Once the time lag and scaling factor have been determined, the present invention copies the speech waveform one time lag earlier to fill the current frame, thus creating an extrapolated waveform. The extrapolated waveform is then scaled with the scaling factor. The present invention also calculates a number of samples of the ringing, or zero-input response, output from the synthesis filter module  195  from the beginning of the current frame. Due to the smoothing effect of the short-term synthesis filter  190 , such a ringing signal will seem to flow smoothly from the decoded speech waveform at the end of the last frame. The present invention then overlap-adds this ringing signal and the extrapolated speech waveform with a suitable overlap-add window in order to smoothly merge these two pieces of waveform. This technique will smooth out waveform discontinuity at the beginning of the current frame. At the same time, it avoids the additional delays created by G.711 Appendix I or the approach of Goodman. 
   If the frame erasure has persisted for an extended period of time, the extrapolated speech signal is attenuated toward zero. Otherwise, it will create a tonal or buzzing sound. In the present invention, the waveform envelope is attenuated linearly toward zero if the length of the frame erasure exceeds a certain threshold. The present invention then uses a memory-efficient method to implement this linear attenuation toward zero. 
   After the waveform extrapolation is performed in the erased frame, the present invention properly updates all the internal memory states of the filters within the speech decoder. If updating is not performed, there would be a large discontinuity and an audible glitch at the beginning of the next good frame. In updating the filter memory after a frame erasure, the present invention works backward from the output speech waveform. The invention sets the filter memory contents to be what they would have been at the end of the current frame, if the filtering operations of the speech decoder were done normally. That is, the filtering operations are performed with a special excitation such that the resulting synthesized output speech waveform is exactly the same as the extrapolated waveform calculated above. 
   As an example, if the short-term predictor  120  is of an order M, then the memory of the short-term synthesis filter  190 , after the FEC operation for the current frame, is simply the last M samples of the extrapolated speech signal for the current frame with the order reversed. This is because the short-term synthesis filter  190  in the conventional decoder  100  is an all-pole filter. The filter memory is simply the previous filter output signal samples in reverse order. 
   An example of updating the memory of the FIR long-term predictor  140  will be presented. In this example, the present invention performs short-term prediction error filtering of the extrapolated speech signal of the current frame, with initial memory of the short-term predictor  120  set to the last M samples (in reverse order) of the output speech signal in the last frame. 
   Similarly, if quantizers for side information (such as LSP and excitation gain) use inter-frame predictive coding, then the memories of those predictors are also updated based on the same principle to minimize the discontinuity of decoded speech parameters at the next good frame. 
   The general principles of the present invention outlined above are applicable to almost any predictive speech decoder. What will be described in greater detail below is a particular implementation of those general principles, in a preferred embodiment of the present invention applied to the decoder of a two-stage noise feedback codec. 
     FIG. 2  is a block diagram illustration of an exemplary embodiment of the present invention. In  FIG. 2 , a conventional predictive speech decoder is shown. The decoder can be, for example, the decoder  100  shown in FIG.  1 ., which includes a filter memory  201  and an input frame erasure flag  200 . If the input frame erasure flag  200  indicates that the current frame received is a good frame, the decoder  100  performs normal decoding operations as described above. During the normal decoding operations, a switch  202  is in an upper position  203  indicating a received good frame, and the decoded speech waveform sq(n) is used as the output of the decoder  100 . Furthermore, the current frame of decoded speech sq(n) is also passed to a speech storage module  204 , which stores the previously decoded speech waveform samples in a buffer. The current frame of decoded speech sq(n) is used to update that buffer. The remaining modules in  FIG. 2  are inactive when a good frame is received. 
   On the other hand, if the input frame erasure flag  200  indicates that a bad frame has been received or that the current frame is not received (e.g., erased or lost), the operation of the decoder  100  is halted, and the switch  202  is set to a lower position  205 . The remaining modules of  FIG. 2  then perform FEC operations to produce an output speech waveform sq′(n) for the current frame, and also update the filter memory  201  of the decoder  100  to prepare the decoder  100  for the normal decoding operations of the next received good frame. When the switch  202  is set to the lower position  205 , the remaining modules shown in  FIG. 2  operate in the following manner. 
   A ringing calculator  206  calculates L samples of ringing, or zero-input response, of the synthesis filter module  195  of  FIG. 1 . A simpler approach is to use only the short-term synthesis filter  190 , but the preferred approach, at least for voiced speech, is to use the ringing of the cascaded long-term synthesis filter  180  and the short-term synthesis filter  190 . This calculation is performed in the following manner. Beginning with the memory  201  of the synthesis filter module  195  left in the delay line after the processing of the last frame, filtering operations are performed for L samples while using a zero input signal to the filter  195 . The resulting L samples of the filter output signal form the desired ringing signal. These L samples of the ringing signal, {r(n), n=1, 2, . . . , L}, are stored for later use. 
   A preliminary time lag module  208  analyzes the previously decoded speech waveform samples stored in the speech storage module  204  to determine a preliminary time lag for waveform extrapolation in the current frame. This can be done in a number of ways, for example, using the approaches outlined by Goodman. The present invention searches for a pitch period pp in the general sense, as in a pitch-prediction-based speech codec. If the conventional decoder  100  has a decoded pitch period of the last frame, and if it is deemed reliable, then the time lag module  208  can simply search around the neighborhood of this pitch period pp to find a suitable time lag. If the decoder  100  does not provide a decoded pitch period, or if this pitch period is deemed unreliable, then the preliminary time lag module  208  can perform a full-scale pitch estimation to get a desired time lag. In  FIG. 2 , it is assumed that such a decoded pp is indeed available and reliable. In this case, the preliminary time lag module  208  operates as follows. 
   First, the preliminary time lag module  208  determines the pitch period of the last frame (pplast). It sets pplast=pp=the decoded pitch period of last frame, if the last frame is a good frame. It sets pplast=the preliminary pitch period (pfep) of the last frame (output from the time lag module  208 ) if the last frame is a bad frame. If, for example, pplast is smaller than 10 ms (80 samples and 160 samples for 8 kHz and 16 kHz sampling rates, respectively), the time lag module  208  uses it as an analysis window size K. If pplast is greater than 10 ms, the time lag module  208  uses 10 ms as the analysis window size K. 
   The preliminary time lag module  208  then determines the pitch search range. To do this, it subtracts 0.5 ms (4 samples and 8 samples for 8 kHz and 16 kHz sampling, respectively) from pplast, compares the result with the minimum allowed pitch period in the codec, and chooses the larger of the two as a lower bound lb of the search range. It then adds 0.5 ms to pplast, compares the result with the maximum allowed pitch period in the codec, and chooses the smaller of the two as the upper bound ub of the search range. 
   An sq(n) buffer within the speech storage module  204  stores N+N f  samples of speech, where the samples sq(n), n=1, 2, . . . , N correspond to the decoder output speech for previous frames, with sq(N) being the last sample of decoded speech in the last frame. N f  is the number of samples in a frame. The storage space sq(n), n=N+1, N+2, . . . , N+N f  are unpopulated at the beginning of a bad frame, but will be filled with extrapolated speech waveform samples once the operations of modules  208  through  220  are completed. 
   For time lags j=lb, lb+1, lb+2, . . . , ub−1, ub, the preliminary time lag module  208  calculates the correlation value 
             c   ⁢     (   j   )       =       ∑     n   =     N   -   K   +   1       N     ⁢       sq   ⁢     (   n   )       ⁢     sq   ⁢     (     n   -   j     )                 
for jε[lb,ub]. Among those time lags that give a positive correlation c(j), the time lag module  208  finds the time lag j that maximizes
 
   
     
       
         
           
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   The division operation above can be avoided by a cross-multiply method. The time lag j that maximizes nc(j) is also the lag time within the search range that maximizes the pitch prediction gain for a single-tap pitch predictor. The optimal time lag ppfep, denotes pitch period for frame erasure, preliminary version. In the extremely rare case where no c(j) in the search range is positive, ppfep is set to equal lb in this degenerate case. 
   If this time lag is used directly as the time lag for periodic repetition in waveform extrapolation of the current frame, buzzing sounds can occur when a small time lag is used in a segment of speech that does not have a high degree of periodicity. To combat this problem, the present invention employs a periodic extrapolation flag module  210  to distinguish between highly periodic voiced speech segments and other types of speech segments. If the extrapolation flag module  210  determines that the decoded speech is, for example, within a highly periodic voiced speech region, it sets the periodic waveform extrapolation flag (pwef) to 1; otherwise, pwef is set to 0. If pwef is 0, then a final time lag and scaling factor module  212  will determine another larger time lag to reduce or eliminate the buzzing sound. 
   Using ppfep as its input, the extrapolation flag module  210  performs a further analysis of the previously decoded speech sq(n) to determine the proper setting of the periodic waveform extrapolation flag pwef. Again, this can be done in a number of different ways. Described below is merely one example. The extrapolation flag module  210  first sets the pwef to its default value of 1, then it calculates the speech energy E in the analysis window: 
   
     
       
         
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   If E is smaller than a certain threshold E 0 , then the pwef is set to 0. An appropriate value of E 0  may be 2 11  K if the input signal samples are represented as 16-bit signed integers. If E&gt;E 0 , then the module  210  further calculates the first normalized autocorrelation coefficient 
   
     
       
         
           
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   If ρ 1  is less than a threshold of, say, T 1 =0.4, the pwef is set to 0; otherwise, the module  210  checks whether the following inequality is true: 
   
     
       
         
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   Exemplary values of the parameters are T 1 =0.4, T 2 =0.99, F 1 =2.0, and F 2 =1.1. If this inequality is true, then the pwef is set to 0. If pwef survives all three tests above, its value remains at the default value of 1. 
   The inequality above can be understood as follows. Assume that E−nc(ppfep)≠0, which is generally true unless the signal energy E itself is zero. Dividing both sides of the inequality by E−nc(ppfep) yields: 
   
     
       
         
           
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   The ratio on the left-hand side is the “single-tap pitch prediction gain” in the linear domain (rather than log domain) for the decoded speech in the analysis window n Eε[(N−K+1),N], when the pitch period is ppfep. The expression on the right-hand side is a linear function of ρ 1 , or y=f(x)=f(ρ 1 ), representing a straight line passing through the two points (T 1 ,F 1 ) and (T 2 ,F 2 ) in the X-Y plane. With the exemplary parameter values given above, if ρ 1 =0.4, the threshold for the pitch prediction gain is 2.0 in the linear domain. If the pitch prediction gain is less than this threshold of 2.0, the decoded speech in the analysis window is not considered to be highly periodic voiced speech, and pwef is set to 0. This threshold is reduced to 1.1 if ρ 1 =0.99. If ρ 1  is between 0.4 and 0.99, then the threshold is determined by the straight line connecting (0.4, 2.0) and (0.99, 1.1). The idea is that when the first normalized autocorrelation coefficient ρ 1  is smaller, the pitch prediction gain threshold is required to be larger, and vice versa. This threshold is adaptive according to the value of ρ 1 . 
   Based on the preliminary time lag ppfep and the periodic waveform extrapolation flag pwef, the final time lag and scaling factor module  212  determines the final time lag and scaling factor for waveform extrapolation in the current frame. 
   If pwef=1, or if ppfep is no smaller than a threshold T 0 , then ppfep is used as the final time lag, i.e., ppfe=ppfep, and the scaling factor ptfe (for pitch tap for frame erasure) is calculated as 
   
     
       
         
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                     n 
                     = 
                     
                       N 
                       - 
                       K 
                       + 
                       1 
                     
                   
                   N 
                 
                 ⁢ 
                 
                    
                   
                     sq 
                     ⁢ 
                     
                       ( 
                       
                         n 
                         - 
                         ppfe 
                       
                       ) 
                     
                   
                    
                 
               
             
             . 
           
         
       
     
   
   The denominator in the equation above is typically non-zero. In the degenerate case when it is zero, then ptfe is also set to zero. If ptfe&gt;1.1, then ptfe is set to 1.1 to avoid ramping up extrapolated waveform too fast. A suitable value of T 0  is the number of samples corresponding to a 10 ms time interval. 
   The scaling factor ptfe calculated above is normally positive. However, in the rare case when c(ppfe), the correlation value at time lag ppfe, is negative, as discussed above with regard to the preliminary time lag module  208 , then the scaling factor ptfe calculated above should be negated. If the negated value is less than −1, it is clipped at −1. 
   If pwef=0 and ppfep&lt;T 0 , there is a higher likelihood for periodic waveform extrapolation to produce a buzz sound. To avoid the potential buzzing sound, the present invention searches for another suitable time lag ppfe≧T 0 . By requiring the time lag ppfe to be large enough, the likelihood of a buzzing sound is greatly reduced. To minimize the potential quality degradation caused by a misclassification of a periodic voiced speech segment into something that is not, the present invention searches in the neighborhood of the first integer multiple of ppfep that is no smaller than T 0 . That way, even if the pwef should have been 1 and is misclassified as 0, there is a good chance that an integer multiple of the true pitch period will be chosen as the final time lag for periodic waveform extrapolation. 
   The module  212  determines the final time lag ppfe and scaling factor ptfe in the following way if pwef=0 and ppfep&lt;T 0 . First, it finds the smallest integer m that satisfies the expression
 
m×ppfep≧T 0 .
 
   Then, it sets m 1 , the lower bound of the time lag search range, to m×ppfep−3 or T 0 , whichever is larger. The upper bound of the search range is set to m 2 =m 1 +N s −1, where N s  is the number of possible time lags in the search range. Next, for each time lag j in the search range of [m 1 ,m 2 ], the module  212  calculates 
               D   ⁢     (   j   )       =       ∑     n   =   1     d     ⁢       (       sq   ⁢     (     N   +   n   -   j     )       -     r   ⁢     (   n   )         )     2         ,         
and then selects the time lag jε[m 1 ,m 2 ] that minimizes D(j). Basically, the search looks for a piece of previously decoded speech waveform that is closest to the first d samples of the ringing of the synthesis filter. Normally d&lt;L, and a possible value for d is 2. The time lag j that minimizes D(j) above is chosen as the final time lag ppfe. The corresponding scaling factor is calculated as
 
   
     
       
         
           ptfe 
           = 
           
             
               
                 
                   ∑ 
                   
                     n 
                     = 
                     1 
                   
                   d 
                 
                 ⁢ 
                 
                    
                   
                     r 
                     ⁢ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                    
                 
               
               
                 
                   ∑ 
                   
                     n 
                     = 
                     1 
                   
                   d 
                 
                 ⁢ 
                 
                    
                   
                     sq 
                     ⁢ 
                     
                       ( 
                       
                         N 
                         + 
                         n 
                         - 
                         ppfe 
                       
                       ) 
                     
                   
                    
                 
               
             
             . 
           
         
       
     
   
   Again, in the degenerate case when the denominator of the equation above is zero, ptfe is also set to zero. In addition, if the ptfe calculated this way is greater than 1.3, then it is clipped to 1.3. 
   After ppfe and ptfe are both determined, an L samples speech extrapolation module  214  extrapolates the first L samples of speech in the current frame. A possible value of L is 5 samples. The extrapolation of the first L samples of the current frame can then be expressed as
 
 sq ( n )=ptfe× sq ( n −ppfe), for n=N+1, N+2, . . . , N+L.
 
   For the first L samples of the current frame, an overlap-adder  216  smoothly merges the sq(n) signal extrapolated above with r(n), the ringing of the synthesis filter calculated in the ringing calculator  206 , using the overlap-add method below.
 
 sq ( N+n )← w   u ( n ) sq ( N+n )+ w   d ( n ) r ( n ), for n=1, 2, . . . , L.
 
   In the equation above, the sign “←” means the quantity on its right-hand side overwrites the variable values on its left-hand side. The window function w u (n) represents the overlap-add window that is ramping up, while w d (n) represents the overlap-add window that is ramping down. These overlap-add windows satisfies the constraint:
 
 w   u ( n )+ w   d ( n )=1
 
   A number of different overlap-add windows can be used. For example, the raised cosine window mentioned in the paper by Goodman can be used here. Alternatively, simpler triangular windows can also be used. 
   After the first L samples of the current frame are extrapolated and overlap-added, a remaining samples speech extrapolator  218  then extrapolates the remaining samples of the current frame. If ppfe≧N f , the extrapolation is performed as
 
 sq ( n )=ptfe× sq ( n −ppfe), for n=N+L+1, N+L+2, . . . , N+N f .
 
If ppfe&lt;N f , then the extrapolation is performed as
 
 sq ( n )=ptfe× sq ( n −ppfe), for n=N+L+1, N+L+2, . . . , N+ppfe, and then
 
 sq ( n )= sq ( n −ppfe), for n=N+ppfe+1, N+ppfe+2, . . . , N+N f .
 
   The elimination of the scaling factor ptfe from the second cycle on is to avoid too much waveform magnitude growth due to extrapolation of high-pitched speech (low pitch period) during extended frame erasure. 
   If the frame erasure lasts for an extended time period, the FEC scheme should not continue the periodic extrapolation indefinitely, otherwise the extrapolated speech begins to resemble the sound of a steady tone signal. In the preferred embodiment of the present invention, a waveform attenuator  220  starts waveform attenuation at the instant when the frame erasure has lasted for 20 ms. From there, the envelope of the extrapolated waveform is attenuated linearly toward zero and the waveform magnitude reaches zero at 60 ms into the erasure of consecutive frames. After 60 ms, the output is completely muted. An exemplary attenuation technique performed in accordance with the present invention is shown in  FIG. 3(   a ). 
   The preferred embodiment of the present invention can be used with a noise feedback codec that has, for example, a frame size of 5 ms. In this case, the time interval between each adjacent pair of vertical lines in  FIG. 3(   a ) represent a frame. 
   If a frame erasure lasts, for example, for 12 consecutive frames (5×12=60 ms) or more, the easiest way to implement this waveform attenuation is to extrapolate speech for the first 12 erased frames, store the resulting 60 ms of waveform, and then apply the attenuation window in  FIG. 3(   a ). However, this simple approach requires extra delay to buffer up 60 ms of extrapolated speech. 
   To avoid any additional delay, the waveform attenuator  220  in  FIG. 2  applies the waveform attenuation window frame-by-frame without any additional buffering. However, starting from the sixth consecutive erased frame, from 25 ms on in  FIG. 3(   a ), the attenuator  220  cannot directly apply the corresponding section of the window for that frame in  FIG. 3(   a ). A waveform discontinuity will occur at the frame boundary, because the corresponding section of the attenuation window starts from a value less than unity (⅞, 6/8, ⅝, etc.). This will cause a sudden decrease of waveform sample value at the beginning of the frame, and thus an audible waveform discontinuity. 
   To eliminate this problem, the present invention normalizes each 5 ms section of the attenuation window in  FIG. 3(   a ) by its starting value at the left edge. For example, for the sixth frame (25 ms to 30 ms), the window is from ⅞ to 6/8, and normalizing this section by ⅞ will give a window from 1 to ( 6/8)1(⅞)= 6/7. Similarly, for the seventh frame (30 ms to 35 ms), the window is from 6/8 to ⅝, and normalizing this section by 6/8 will give a window from 1 to (⅝)1( 6/8)=⅚. Such a normalized attenuation window for each frame is shown in  FIG. 3(   b ). 
   As illustrated in  FIG. 3(   b ), rather than storing every sample in the normalized attenuation window, the present invention can simply store the decrement between adjacent samples of the window for each of the eight window sections from fifth to twelfth frame. This decrement is the amount of total decline of the window function in each frame (⅛ for the fifth erased frame, 1/7 for the sixth erased frame, and so on), divided by N f , the number of speech samples in a frame. 
   In the example above, if the frame erasure has lasted for only 20 ms or less, the waveform attenuator  220  does not need to perform any waveform attenuation operation. If the frame erasure has lasted for more than 20 ms, then the attenuator  220  applies the appropriate section of the normalized waveform attenuation window in  FIG. 3(   b ), depending on how many consecutive frames have been erased so far. For example, if the current frame is the sixth consecutive frame that is erased, then the attenuator  220  applies the section of the window from 25 ms to 30 ms (with window function from 1 to 6/7). Since the normalized waveform attenuation window for each frame always starts with unity, the windowing operation will not cause any waveform discontinuity at the beginning of the frame. 
   The normalized window function is not stored. Instead, it is calculated on the fly. Starting with a value of 1, the attenuator  220  multiplies the first waveform sample of the current frame by 1, and then reduces the window function value by the decrement value calculated and stored beforehand, as mentioned above. It then multiplies the second waveform sample by the resulting decremented window function value. The window function value is again reduced by the decrement value, and the result is used to scale the third waveform sample of the frame. This process is repeated for all samples of the extrapolated waveform in the current frame. 
   The waveform attenuator  220  produces the output sq′(n) for the current erased frame, as shown in  FIG. 2 . The output sq′(n) is passed through switch  202  and becomes the final output speech for the current erased frame. The current frame of sq′(n) is passed to the speech storage module  204  to update the current frame portion of the sq(n) speech buffer stored there. Let sq′(n), n=1, 2, . . . , N f  be the output of the waveform attenuator  220  for the current erased frame, then the sq(n) buffer of the speech storage module  204  is updated as:
 
 sq ( N+n )= sq ′( n ),  n= 1, 2, . . . ,  N   f .
 
   This signal sq′(n) is also passed to a filter memory update module  222  to update the memory  201 , or internal states, of the filters within the conventional decoder  100 . The filter memory update is performed in order to ensure the filter memory is consistent with the extrapolated speech waveform in the current erased frame. This is necessary for a smooth transition of speech waveform at the beginning of the next frame, if the next frame turns out to be a good frame. If the filter memory  201  were frozen without such proper update, then generally there would be audible glitch or disturbance at the beginning of the next good frame. 
   In updating the filter memory  201  after a frame erasure, the filter memory update module  222  works backward from the updated speech buffer sq(n) in the conventional decoder  100 . If the short-term predictor is of order M, then the updated memory is simply the last M samples of the extrapolated speech signal for the current erased frame, but with the order reversed. Let stsm(k) be the k-th memory value of the short-term synthesis filter  190  of  FIG. 1 , or the value stored in the delay line corresponding to the k-th short-term predictor  120  coefficient a k . Then, the memory  201  of the short-term synthesis filter is updated as
 
 stsm ( k )= sq ( N+N   f +1− k ), k=1, 2, . . . , M.
 
   To update the memory  201  of the FIR long-term predictor  140 , the filter memory update module  222  performs short-term prediction error filtering of the extrapolated speech signal of the current frame, with initial memory of the short-term predictor  120  set to the last M samples of the output speech signal in the last frame, with the order reversed. More specifically, let stpm(k) be the k-th memory value for the short-term prediction error filter, then such memory is initialized as
 
 stpm ( k )= sq ( N+ 1− k ), k=1, 2, . . . , M
 
The short-term predictor  120  has a transfer function of
 
   
     
       
         
           
             A 
             ⁢ 
             
               ( 
               z 
               ) 
             
           
           = 
           
             1 
             - 
             
               
                 ∑ 
                 
                   k 
                   = 
                   1 
                 
                 M 
               
               ⁢ 
               
                 
                   a 
                   k 
                 
                 ⁢ 
                 
                   z 
                   
                     - 
                     k 
                   
                 
               
             
           
         
       
     
   
   With stpm(k), k=1, 2, . . . , M as the initial filter memory of A(z), the filter memory update module  222  passes the extrapolated speech for the current erased frame, sq′(n), n=1, 2, . . . , N f  through this filter A(z). The corresponding N f  samples at the output of this filter A(z) are used to update the current frame portion of the memory of the FIR long-term predictor  140 . 
   If none of the side information speech parameters (LPC, pitch period, pitch taps, and excitation gain) is quantized using predictive coding, the operations of the filter memory update module  222  are completed. If, on the other hand, predictive coding is used for side information, then the filter memory update module  222  also needs to update the memory of the involved predictors to minimize the discontinuity of decoded speech parameters at the next good frame. 
   In an exemplary noise feedback codec that the preferred embodiment of the present invention can be used in, moving-average (MA) predictive coding is used to quantize both the Line-Spectrum Pair (LSP) parameters and the excitation gain. The predictive coding schemes for these parameters work as follows. For each parameter, the long-term mean value of that parameter is calculated off-line and subtracted from the unquantized parameter value. The predicted value of the mean-removed parameter is then subtracted from this mean-removed parameter value. A quantizer (not shown) quantizes the resulting prediction error. The output of the quantizer is used as the input to an associated MA predictor (not shown). The predicted parameter value and the long-term mean value are both added back to the quantizer output value to reconstruct a final quantized parameter value. 
   In an embodiment of the present invention, the modules  208  through  220  produce the extrapolated speech for the current erased frame. Theoretically, for the current frame, there is no need to extrapolate the side information speech parameters since the output speech waveform has already been generated. However, to ensure that the LSP and gain decoding operations will go smoothly at the next good frame, it is helpful to assume that these parameters are extrapolated from the last frame. This can be done by simply copying the parameter values from the last frame, and then working “backward” from these extrapolated parameter values to update the predictor memory of the predictive quantizers for these parameters. 
   Using the principle outlined above, a predictor memory in a predictive LSP quantizer can be updated as follows. For the k-th LSP parameter, its predicted value can be calculated as the inner product of the predictor coefficient array and the predictor memory array for the k-th LSP parameter. This predicted value and the long-term mean value of the k-th LSP are then subtracted from the k-th LSP parameter value at the last frame. The resulting value is used to update the newest memory location for the predictor of the k-th LSP parameter (after the original set of predictor memory is shifted by one memory location, as is well-known in the art). This procedure is repeated for all the LSP parameters (there are M of them). 
   If the frame erasure lasts only 20 ms or less, no waveform attenuation window is applied, and it is assumed that the excitation gain of the current erased frame is the same as the excitation gain of the last frame. In this case, the memory update for the gain predictor is essentially the same as the memory update for the LSP predictors described above. Basically, the predicted value of log-gain is calculated by calculating the inner product of the predictor coefficient array and the predictor memory array for the log-gain. This predicted log-gain and the long-term mean value of the log-gain are then subtracted from the log-gain value of the last frame. The resulting value is used to update the newest memory location for the log-gain predictor (after the original set of predictor memory is shifted by one memory location, as is well-known in the art). 
   If the frame erasure lasts more than 60 ms, the output speech is zeroed out, and the base-2 log-gain is assumed to be at an artificially set default silence level of −2.5. Again, the predicted log-gain and the long-term mean value of log-gain are subtracted from this default level of −2.5, and the resulting value is used to update the newest memory location for the log-gain predictor. 
   If the frame erasure lasts more than 20 ms but does not exceed 60 ms, then updating the predictor memory for the predictive gain quantizer is challenging because the extrapolated speech waveform is attenuated using the waveform attenuation window of  FIGS. 3(   a ) and ( b ). The log-gain predictor memory is updated based on the log-gain value of the waveform attenuation window in each frame. 
   To minimize the code size, for each of the frames from the fifth to the twelfth frames into frame erasure, a correction factor from the log-gain of the last frame can be precalculated based on the attenuation window of  FIG. 3(   a ) and ( b ). The correction factor is then stored. The following algorithm calculates these 8 correction factors, or log-gain attenuation factors.
         1. Initialize lastlg=0. (lastlg=last log-gain=log-gain of the last frame)   2. Initialize j=1.   3. Calculate the normalized attenuation window array       

   
     
       
         
           
             
               w 
               ⁢ 
               
                 ( 
                 n 
                 ) 
               
             
             = 
             
               1 
               - 
               
                 
                   n 
                   - 
                   1 
                 
                 
                   
                     ( 
                     
                       9 
                       - 
                       j 
                     
                     ) 
                   
                   ⁢ 
                   
                     N 
                     f 
                   
                 
               
             
           
           , 
           
             n 
             = 
             1 
           
           , 
           2 
           , 
           … 
           ⁢ 
           
               
           
           , 
           
             
               N 
               f 
             
             . 
           
         
       
     
   
   
     
       
         
           
             4. 
             ⁢ 
             
                 
             
             ⁢ 
             
               Calculate 
             
             ⁢ 
             
                 
             
             ⁢ 
             lg 
           
           = 
           
             2 
             ⁢ 
             
               
                 log 
                 2 
               
               ⁡ 
               
                 [ 
                 
                   
                     1 
                     
                       N 
                       f 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         1 
                       
                       
                         N 
                         f 
                       
                     
                     ⁢ 
                     
                       
                         w 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
       
       
         
           5. Calculate lga(j)=lastlg−lg 
         
       
     
  
   
     
       
         
           
             
               6. 
               ⁢ 
               
                   
               
               ⁢ 
               
                 If  
               
               ⁢ 
               
                   
               
               ⁢ 
               j 
             
             &lt; 
             8 
           
           , 
           
             
               
                 then  set 
               
               ⁢ 
               
                   
               
               ⁢ 
               lastlg 
             
             = 
             
               lg 
               - 
               
                 2 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     log 
                     2 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         8 
                         - 
                         j 
                       
                       
                         9 
                         - 
                         j 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
       
       
         
           7. If j=8, stop; otherwise, increment j by 1 (i.e., j←j+1), then go back to step 3. 
         
       
     
  
   The algorithm above calculates the base-2 log-gain value of the waveform attenuation window for a given frame. It then determines the difference between this value and a similarly calculated log-gain for the window of the previous frame, compensated for the normalization of the start of the window to unity for each frame. The output of this algorithm is the array of log-gain attenuation factors lga(j) for j=1, 2, . . . , 8. Note that lga(j) corresponds to the (4+j)-th frame into frame erasure. 
   Once the lga(j) array has been pre-calculated and stored, then the log-gain predictor memory update for frame erasure lasting 20 ms to 60 ms becomes straightforward. If the current erased frame is the j-th frame into frame erasure (4&lt;j≦12), lga(j−4) is subtracted from the log-gain value of the last frame. From the result of this subtraction, the predicted log-gain and the long-term mean value of log-gain are subtracted, and the resulting value is used to update the newest memory location for the log-gain predictor. 
   After the filter memory update module  222  calculates all the updated filter memory values, the conventional decoder  100  uses these values to update the memory  201 . In particular, it updates the memory of its short-term synthesis filter  190 , its long-term synthesis filter  180 , and all of the predictors, if any, used in side information quantizers, in preparation for the decoding of the next frame, assuming the next frame will be received intact. 
     FIGS. 4(   a ) and  4 ( b ) provide an exemplary method of practicing the preferred embodiment of the present invention. The present invention begins by storing samples of the output decoded signal in a memory, as indicated in block  400 . The decoded speech waveform, output from the decoder  100 , is analyzed and the preliminary time lag value is determined in block  402 . Next, the signal output from the operation of the block  402  is analyzed and classified to determine whether or not periodic repetition can be performed. If the signal is determined to be sufficiently periodic, the periodic repetition flag is set, and the final time lag and the scaling factor are determined as indicated in blocks  404  and  406  respectively. 
   After determination of the final time lag and the scaling factor, the present invention extrapolates L samples of speech and calculates L samples of ringing of the synthesis filter module  195 , based upon the determined final time lag and the determined scaling factor, as shown in blocks  408  and  410  respectively. The L extrapolated samples and the L samples of ringing of the synthesis filter are then overlap-added as indicated in block  412 . The remaining samples are then extrapolated as indicated in block  414 . The blocks  408 ,  410 ,  412 , and  414  cooperatively function to remove potential discontinuities between frames. If frame erasure continues, a waveform attenuation process is initiated in block  416 . Finally, the memory of the filters is updated to ensure that its contents are consistent with the extrapolated speech waveform in the current erased frame, as shown in block  418 , and the process ends. 
   The following description of a general purpose computer system is provided for completeness. As stated above, the present invention can be implemented in hardware, or as a combination of software and hardware. Consequently, the invention may be implemented in the environment of a computer system or other processing system. An example of such a computer system  500  is shown in  FIG. 5 . In the present invention, all of the elements depicted in  FIGS. 1 and 2 , for example, can execute on one or more distinct computer systems  500 , to implement the various methods of the present invention. 
   The computer system  500  includes one or more processors, such as a processor  504 . The processor  504  can be a special purpose or a general purpose digital signal processor and it&#39;s connected to a communication infrastructure  506  (for example, a bus or network). Various software implementations are described in terms of this exemplary computer system. After reading this description, it will become apparent to a person skilled in the relevant art how to implement the invention using other computer systems and/or computer architectures. 
   The computer system  500  also includes a main memory  508 , preferably random access memory (RAM), and may also include a secondary memory  510 . The secondary memory  510  may include, for example, a hard disk drive  512  and/or a removable storage drive  514 , representing a floppy disk drive, a magnetic tape drive, an optical disk drive, etc. The removable storage drive  514  reads from and/or writes to a removable storage unit  518  in a well known manner. The removable storage unit  518 , represents a floppy disk, magnetic tape, optical disk, etc. which is read by and written to by removable storage drive  514 . As will be appreciated, the removable storage unit  518  includes a computer usable storage medium having stored therein computer software and/or data. 
   In alternative implementations, the secondary memory  510  may include other similar means for allowing computer programs or other instructions to be loaded into the computer system  500 . Such means may include, for example, a removable storage unit  522  and an interface  520 . Examples of such means may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an EPROM, or PROM) and associated socket, and the other removable storage units  522  and the interfaces  520  which allow software and data to be transferred from the removable storage unit  522  to the computer system  500 . 
   The computer system  500  may also include a communications interface  524 . The communications interface  524  allows software and data to be transferred between the computer system  500  and external devices. Examples of the communications interface  524  may include a modem, a network interface (such as an Ethernet card), a communications port, a PCMCIA slot and card, etc. Software and data transferred via the communications interface  524  are in the form of signals  528  which may be electronic, electromagnetic, optical or other signals capable of being received by the communications interface  524 . These signals  528  are provided to the communications interface  524  via a communications path  526 . The communications path  526  carries the signals  528  and may be implemented using wire or cable, fiber optics, a phone line, a cellular phone link, an RF link and other communications channels. 
   In the present application, the terms “computer readable medium” and “computer usable medium” are used to generally refer to media such as the removable storage drive  514 , a hard disk installed in the hard disk drive  512 . These computer program products are means for providing software to the computer system  500 . 
   Computer programs (also called computer control logic) are stored in the main memory  508  and/or the secondary memory  510 . Computer programs may also be received via the communications interface  524 . Such computer programs, when executed, enable the computer system  500  to implement the present invention as discussed herein. 
   In particular, the computer programs, when executed, enable the processor  504  to implement the processes of the present invention. Accordingly, such computer programs represent controllers of the computer system  500 . By way of example, in the embodiments of the invention, the processes/methods performed by signal processing blocks of encoders and/or decoders can be performed by computer control logic. Where the invention is implemented using software, the software may be stored in a computer program product and loaded into the computer system  500  using the removable storage drive  514 , the hard drive  512  or the communications interface  524 . 
   In another embodiment, features of the invention are implemented primarily in hardware using, for example, hardware components such as Application Specific Integrated Circuits (ASICs) and gate arrays. Implementation of a hardware state machine so as to perform the functions described herein will also be apparent to persons skilled in the relevant art(s). 
   The foregoing description of the preferred embodiments provide an illustration and description, but is not intended to be exhaustive or to limit the invention to the precise form disclosed. Modifications and variations are possible consistent with the above teachings, or may be acquired from practice of the invention.