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In digital speech communication, transmission errors generally introduce impulsive distortions in the received speech waveform. Smoothing of this waveform results at once in a squelching of the distortion component, and in an undesirable smearing of the speech. However, our experience with practical differential PCM (DPCM) codes (with adaptive quantizers and first-order predictors) has shown that if the error probability is fairly significant (for example, 0.025), the noise attenuation is perceptually desirable in spite of the attendant speech-muffling. Our observations are based on computer simulations and informal listening tests. The smoothing can be performed either on the received DPCM word (prediction error signal) or the reconstructed speech amplitude. (The two signals are identical in nondifferential PCM.) Smoothing algorithms can be either linear (based, for example, on running averages) or nonlinear (based, for example, on running medians). Studies with 3-bit quantizers indicate that with independently occurring transmission errors, smoothing of the prediction error signal is perceptually desirable, although the benefits decrease as a function of the predictor coefficient a, with the maximum advantage showing up for (PCM). Running averages and running medians seem to work equally well, and suggested block lengths for their computations are three or five samples. Results with clustered transmission errors show a higher advantage due to smoothing and a preference of linear methods and longer block lengths.