A comparative study of least-squares and homomorphic techniques for the inversion of mixed phase signals

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Abstract
The inversion of minimum phase signals is well understood. However, many signals are non-minimum phase and the deconvolution of such sequences is less well documented. The aim of this paper is to compare two of the main techniques for inversion of finite length sequences, namely, homomorphic and least squares. Homomorphic methods require separation of the sequence into minimum and maximum phase components prior to inversion. On the other hand, least squares methods are applicable directly to the time sequence. However, the usual formulation applied to mixed phase signals produces an output having an all-pass form, but the use of delay yields an operator which can approximately invert mixed phase inputs. A brief summary of the two approaches is given, followed by a detailed comparison of the methods as applied to several case studies.

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