From frequency to quefrency: a history of the cepstrum

The idea of the log spectrum or cepstral averaging has been useful in many applications such as audio processing, speech processing, speech recognition, and echo detection for the estimation and compensation of convolutional distortions. To suggest what prompted the invention of the term cepstrum, this article narrates the historical and mathematical background that led to its discovery. The computations of earlier simple echo representations have shown that the spectrum representation domain results does not belong in the frequency or time domain. Bogert et al. (1963) chose to refer to it as quefrency domain and later termed the spectrum of the log of a time waveform as the cepstrum. The article also recounts the analysis of Al Oppenheim in relation to the cepstrum. It was in his theory for nonlinear signal processing, referred to as homomorphic systems, that the realization of the characteristic system of homomorphic convolution was reminiscent of the cepstrum. To retain both the relationship to the work of Bogart et al. and the distinction, the term power cepstrum was eventually applied to the nonlinear mapping in homomorphic deconvolution . While most of the terms in the glossary have faded into the background, the term cepstrum has survived and has become part of the digital signal processing lexicon.