Time-Domain Cepstral Transformations

Document Type

Article

Publication Date

1-1-1993

Abstract

This paper addresses the realization of homomorphic systems for convolution. The motivation for the work comes from the limitations of the method commonly used in homomorphic (complex cepstral) filtering, which is based on the application of the Fourier transform. The calculation of the unwrapped phase, the effects of regions with low signal-to-noise ratios (and spectral notching), aliasing, windowing, and signal truncation effects are some common limitations of the Fourier transform (FT) method. We introduce a new method, time-domain cepstral transformation (TDCT), that is entirely based on time-domain calculations. It thus avoids or minimizes the problems associated with the FT method. Explicit transformations of an ordinary mixed phase time sequence (belonging to convolution space) into its complex cepstrum time sequence (belonging to additive cepstrum vector space) and vice versa are derived. The TDCT method does not require unwrapped phase calculations and no specific windows are used to precondition the signal in order to produce a more accurate representation of the complex cepstrum. The TDCT's are matrix formulas, and their results match well the theoretical complex cepstrum (calculated for known systems). The TDCT method trades reduced computational efficiency for improved performance. Examples are presented comparing Fourier-based and TD cepstrum transformations. © 1993 IEEE

Publication Title

IEEE Transactions on Signal Processing

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