A method and apparatus for shaping the impulse response of a non-minimum phase communications channel, by reversing the CIR without enhancing the noise level using non-causal allpass filters is disclosed. Unstable allpass filters are implemented as stable non-causal filters operating in reversed time to obtain a minimum phase response from a non-minimum phase CIR. The original CIR is estimated using adaptive algorithms, and the coefficients of the allpass filters are taken directly from the estimated CIR. The cascade of the channel and allpass filter has an impulse response that is the approximate time reversed version of the original CIR. A "block" allpass equalizer and an "optimal" allpass equalizer are used in a two-stage filter to increase system performance. Other multiple stage filter configurations are disclosed, which can include use of decision feedback equalizer (DFE) decoders as well as Viterbi decoders. The invention is effective in the case of two-path channels, but can also give satisfactory results when more paths are present. Moreover, the present invention is well suited to "sharpening" the CIR with only minor variations in noise level. A minimum phase desired impulse response (DIR) can be obtained with only a few nonzero samples, leading to a substantial reduction in complexity of the Viterbi algorithm, with only minor variations in the noise level.