The cepstrum: A guide to processing

Abstract

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~.

Time–quefrency analysis of overlapping similar microseismic events

“…The cepstrum shows a clear peak at the interval between similar events. Childers et al (1977) summarised cepstrum analysis. When we apply cepstrum analysis to a proximate microseismic doublet, two peaks are apparent in their cepstrum.…”

“…The inverse Fourier transform of the logarithm of the power spectrum is the cepstrum, which is a function of quefrency (Bogert et al, 1963;Childers et al, 1977;Brockwell and Davis, 2002). The dimension of quefrency is time.…”

“…The cepstrum has higher-order components (Childers et al, 1977), which are artefacts of the true cepstrum peaks. However, the artefacts caused by the higher-order components are smaller than the true cepstrum peaks (Childers et al, 1977). For example, peaks shown at the quefrency of 3.996 and 3.992 s in Figure 8b and at the quefrency of 3.99 s in Figure 9b are the artefacts.…”

Speaker Independent Speech Recognition using MFCC with Cubic-Log Compression and VQ Analysis

“…A logarithmic power spectrum is calculated and declared to be the new analysis window. On that an inverse FFT is performed [19]. The result is a signal with a time axis.…”

The extraction of single-void characteristics from ultrasonic backscatter from void clusters

“…(l2) and noting that the log of a product equals the sum of the logs. Next an inverse FT is applied which gives the complex cepstrum (6). If HC(w) is slowly varying in w and D(w) varies rapidly, the inverse FT will separate them in the cepstrum, and D(w) can then be filtered out using standard linear operations .…”