Cepstrum

A cepstrum (/ˈkɛpstrumˈˌˈsɛpstrumˈ/) is the result of taking the inverse Fourier transform (IFT) of the logarithm of the estimated spectrum of a signal. It may be pronounced in the two ways given, the second having the advantage of avoiding confusion with 'kepstrum' which also exists (see below). There is a complex cepstrum, a real cepstrum, a power cepstrum, and a phase cepstrum. The power cepstrum in particular finds applications in the analysis of human speech.

The name "cepstrum" was derived by reversing the first four letters of "spectrum". Operations on cepstra are labelled quefrency analysis (aka quefrency alanysis), liftering, or cepstral analysis.

The power cepstrum was defined in a 1963 paper by Bogert et al. The power cepstrum of a signal is defined as the squared magnitude of the inverse Fourier transform of the logarithm of the squared magnitude of the Fourier transform of a signal.

A short-time cepstrum analysis was proposed by Schroeder and Noll for application to pitch determination of human speech.

The complex cepstrum was defined by Oppenheim in his development of homomorphic system theory and is defined as the Inverse Fourier transform of the logarithm (with unwrapped phase) of the Fourier transform of the signal. This is sometimes called the spectrum of a spectrum.

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