Cepstrum

The term cepstrum has come to be accepted terminology for the inverse Fourier transform of the logarithm of the power spectrum of a signal. The cepstrum of a complex signal is especially useful in revealing hidden echoes. How does this work? Imagine a complex audio or video signal which is contaminated with echoes. Because the echoes are periodic, once the conversion is made to the frequency domain, the echo periods will show up as low frequency components of the signal. By taking the logarithm of this frequency spectrum, which exaggerates the low-frequencies in favour of the high-frequencies, and converting back to the time-domain, the echoes are more clearly revealed. The term cepstrum is due to Bogert, Healy and Tukey who published a paper with the snappy title "The Quefrency Analysis of Time Series for Echoes: Cepstrum, Pseudoautocovariance, Cross-Cepstrum, and Saphe Cracking"! They arrived at the term cepstrum as an anagram of the word spectrum although, given the fact that the cepstrum is actually a time domain representation and not a frequency base representation, the term mite (an anagram of time) might be more appropriate; even if it sounds less erudite!

Links

Back to Contents

Address all mail to richard@richardbrice.net

Web link richardbrice.net