Cepstrum

In Fourier analysis, the cepstrum (/ˈkɛpstrʌm, ˈsɛp-, -strəm/; plural cepstra, adjective cepstral) is the result of computing the inverse Fourier transform (IFT) of the logarithm of the estimated signal spectrum.

[2] Such effects are related to noticeable echos or reflections in the signal, or to the occurrence of harmonic frequencies (partials, overtones).

[citation needed] The terms "quefrency", "alanysis", "cepstrum" and "saphe" were invented by the authors by rearranging the letters in frequency, analysis, spectrum, and phase.

It can be shown that both formulas are consistent with each other as the frequency spectral distribution remains the same, the only difference being a scaling factor [2] which can be applied afterwards.

[4] It has a focus on periodic effects in the amplitudes of the spectrum:[6] The complex cepstrum was defined by Oppenheim in his development of homomorphic system theory.

[11] The kepstrum, which stands for "Kolmogorov-equation power-series time response", is similar to the cepstrum and has the same relation to it as expected value has to statistical average, i.e. cepstrum is the empirically measured quantity, while kepstrum is the theoretical quantity.

Playing further on the anagram theme, a filter that operates on a cepstrum might be called a lifter.

It was originally invented for characterizing the seismic echoes resulting from earthquakes and bomb explosions.

It has also been used to determine the fundamental frequency of human speech and to analyze radar signal returns.

In particular, the power cepstrum is often used as a feature vector for representing the human voice and musical signals.

Note that a pure sine wave can not be used to test the cepstrum for its pitch determination from quefrency as a pure sine wave does not contain any harmonics and does not lead to quefrency peaks.

[15] A short-time cepstrum analysis was proposed by Schroeder and Noll in the 1960s for application to pitch determination of human speech.