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. The method is a tool for investigating periodic structures in frequency spectra. The power cepstrum has applications in the analysis of human speech. The term cepstrum was derived by reversing the first four letters of spectrum. Operations on cepstra are labelled quefrency analysis (or quefrency alanysis), liftering, or cepstral analysis. It may be pronounced in the two ways given, the second having the advantage of avoiding confusion with kepstrum. The concept of the cepstrum was introduced in 1963 by B. P. Bogert, M. J. Healy, and J. W. Tukey. It serves as a tool to investigate periodic structures in frequency spectra. Such effects are related to noticeable echos or reflections in the signal, or to the occurrence of harmonic frequencies (partials, overtones). Mathematically it deals with the problem of deconvolution of signals in the frequency space. References to the Bogert paper, in a bibliography, are often edited incorrectly. The terms "quefrency", "alanysis", "cepstrum" and "saphe" were invented by the authors by rearranging the letters in frequency, analysis, spectrum, and phase. The invented terms are defined in analogy to the older terms. The cepstrum is the result of following sequence of mathematical operations: transformation of a signal from the time domain to the frequency domain computation of the logarithm of the spectral amplitude transformation to frequency domain, where the final independent variable, the quefrency, has a time scale. The cepstrum is used in many variants. Most important are: power cepstrum: The logarithm is taken from the "power spectrum" complex cepstrum: The logarithm is taken from the spectrum, which is calculated via Fourier analysis The following abbreviations are used in the formulas to explain the cepstrum: The "cepstrum" was originally defined as power cepstrum by the following relationship: The power cepstrum has main applications in analysis of sound and vibration signals.

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Related publications (7)

Cepstral normalisation and the signal to noise ratio spectrum in automatic speech recognition.

Philip Neil Garner

Cepstral normalisation in automatic speech recognition is investigated in the context of robustness to additive noise. It is argued that such normalisation leads naturally to a speech feature based on signal to noise ratio rather than absolute energy (or p ...
Idiap2011

Cepstral normalisation and the signal to noise ratio spectrum in automatic speech recognition

Philip Neil Garner

Cepstral normalisation in automatic speech recognition is investigated in the context of robustness to additive noise. In this paper, it is argued that such normalisation leads naturally to a speech feature based on signal to noise ratio rather than absolu ...
2011

Heat transport in model jammed solids

Matthieu Wyart, Ning Xu

We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and therma ...
2010
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Discrete cosine transform
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including (such as JPEG and HEIF), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).

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