Significance of moment of discrete signals in homomorphic processing

概要

論文の詳細を見る
Moments are known as a set of descriptive constants for both continuous and discrete signals. For the convolution of two discrete signals, it is shown using the frequency domain definition of moment that the moments of cepstrum of the convolution output is the sum of moments of cepstrum of each signal component. Therefore, it is possible to deconvolve the signals in terms of moments. In the conventional homomorphic processing, one is usually concerned with the complex logarithm of the Fourier transform and must ensure its proper handling by using sophisticated algorithms such as phase unwrapping. Further, it is also required to calculate the infinite duration cepstrum using discrete Fourier transform techniques and therefore leads to unavoidable aliasing error. It is shown in this paper that the moments of a signal sequence and of its corresponding cepstral coefficients. Hence an ideal calculation for the moment of 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. Effectiveness of this new method which is based on calculating the moments of a signal sequence and its cepstrum, is demonstrated in the problems of homomorphic deconvolution and echo removal. In linear filters, moments of minimum phase signal are related to moments of the corresponding linear phase signal using cepstral moments.
長岡技術科学大学の論文