Moment of cepstrum and its applications

It is shown that the moments of a signal sequence and of its corresponding cepstral sequence are related in a way which obviates the need for the direct calculation of the cepstral coefficients. Hence, an ideal calculation for the moments of the cepstrum is possible even if the duration of the cepstrum is infinite. It is also possible to describe all the properties of a signal sequence from its moments. The effectiveness of this method is demonstrated in the problems of homomorphic deconvolution and echo removal. It is also shown that in linear filtering problems, the moments of the minimum-phase sequence are calculated from the corresponding linear-phase sequence without actually calculating the minimum-phase sequence. For a discrete-time real signal sequence with finite duration, complete equivalence is demonstrated between the signal sequence and its moments. This permits a new description and a new set of design specifications based on moments for such systems.<
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