The cepstrum and complex demodulation for both wrapped and unwrapped phase outputs are examined as to their performance in the presence of amplitude distortion and dispersion in a channel. With amplitude distortion, complex demodulation is a more powerful processor than cepstrum unless zeros occur in the amplitude spectrum of the distortion. Such singularities disrupt the unwrapped phase output completely and, unless removed, limit the useful region of the wrapped phase output. With phase distortion or dispersion, both the cepstrum and complex demodulation (wrapped phase output) yield biased time delay estimates. A successful phase unwrapping process in complex demodulation enables the correct estimate of the time delay in the presence of dispersion. In addition, the dispersion itself is extracted.