Time-domain cepstral transformations

The realization of homomorphic systems for convolution is addressed, motivated by the limitations of the Fourier-transform-based method commonly used in homomorphic (complex cepstral) filtering. The time-domain cepstral transformation (TDCT) method, which is entirely based on time-domain calculations, thus avoiding or minimizing the problems associated with the FT method, is introduced. 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 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. It trades reduced computational efficiency for improved performance. Examples comparing Fourier-based and TD cepstrum transformations are presented