A least mean-square (LMS) adaptive filtering approach has been formulated for removing the deleterious effects of additive noise on the speech signal. Unlike the classical LMS adaptive filtering scheme, the proposed method is designed to cancel out the clean speech signal. This method takes advantage of the quasi-periodic nature of the speech signal to form an estimate of the clean speech signal at time t from the value of the signal at time t minus the estimated pitch period. For additive white noise distortion, preliminary tests indicate that the method improves the perceived speech quality and increases the signal-to-noise ratio (SNR) by 7 dB in a 0 dB environment. The method has also been shown to partially remove the perceived granularity of CVSD coded speech signals and to lead to an improvement in the linear prediction analysis/synthesis of noisy speech.