The cepstrum function was originally developed for characterizing the seismic echoes resulting from earthquake and bomb explosions. It has also been used to determine the fundamental frequency of human speech, to analyze radar signal returns, and to evaluate machinery vibration.

A cepstrum of time history is calculated as follows:

1. Take the Fourier transform of a time history

2. Take the magnitude of the Fourier transform

3. Take the natural logarithm of the magnitude

4. Take the inverse Fourier transform of the natural logarithm

There are also variations upon the previous steps yielding specialized cepstrum-type functions.

A paper is given at: cepstrum.pdf

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The autocepstrum is defined as the cepstrum of the autocorrelation. The autocepstrum is more accurate than the cepstrum in the analysis of data with echoes.

A paper is given at: auto_cepstrum.pdf

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Matlab scripts for performing both the cepstrum and auto-cepstrum functions are included in: Vibrationdata Signal Analysis Package

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– Tom Irvine

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