Cepstrum

A cepstrum (/ˈkɛpstrʌm, ˈsɛp-, -strəm/) 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 has applications in the analysis of human speech. A cepstrum (/ˈkɛpstrʌm, ˈsɛp-, -strəm/) 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 has 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: