The heuristics of cepstrum analysis of a stationary complex echoed Gaussian signal in stationary Gaussian noise

A&tmct-This paper is a pragmatic tutorial review of the cepstrum litemture focusing on data processing. The power, complex, and phase cepstrr~showntobeerpilyrehtedtooaemother. Roblemsrssodated with plnse unwrqphg, linear phase components, spechum notching, rlhsing, oversunpling, and extending &e data aeqnence with zeros are dixmssed. The advlntaga and di.uddpmtrges of windowing the sampled data sequence, the log s p e c t n m , and the complex cepstrum are pxesented. The iufluence of noise upon the data processing procedures is discussed throughout the paper, but is not thoroughly analyzed. The effects of nrious forms of liftering the cepstnun are desai bed. The d lx obtained by applying whitening and trend removal techniques to the spectrum prior to the alcuhtion of the cep S i N D l U e d i S C U S dWe have attempted to synthesize the results, procedures, and infor-mation~tothemauyfieldsthatareEindingcepstnunamlysis wful. In particubu we discuss the interpretation and F g of data in such areas as speech, -, and hydmacoustm. But we must caution the readex that the paper is heavily influenced by our own experiences; specirk procedures that have been found useful in one field should not be conaidered as totally general to other fields. t~h o p e d t h . t t h i s r w i e w w i l l b e o f n l u e t o t h o s e f~w i t h t h e fi~andreducethetimerequiredforthosewishingtobecome~.

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“…Therefore, if we have the convolution of two sequences, then (2) or I X ( z ) I' = I F(z) I2 * I G(z) I '…”

Section: A the Power Cepstrummentioning

confidence: 99%

“…Noise analysis is presented in a more quantitative and extensive manner in [2], 171, [91, 1121, [26], 1301. We point out in particular that it has been recently shown that S.NR alone is an insufficient measure for determining cepstrum performance and that the relative bandwidths of the signal and noise are also needed [ 71.…”

Section: A the Effects Of Noisementioning

confidence: 99%