Editing Cepstrum (section)

==Related concepts==

{{anchor|Quefrency}}The [[Dependent and independent variables|independent variable]] of a cepstral graph is called the '''quefrency'''.<ref name="Steinbuch-Weber_1974">{{cite book |title=Taschenbuch der Informatik – Band III – Anwendungen und spezielle Systeme der Nachrichtenverarbeitung |language=German |editor-first1=Karl W. |editor-last1=Steinbuch |editor-link1=Karl W. Steinbuch |editor-first2=Wolfgang |editor-last2=Weber |editor-first3=Traute |editor-last3=Heinemann |date=1974 |orig-year=1967 |edition=3 |volume=3 |work=Taschenbuch der Nachrichtenverarbeitung |publisher=[[Springer Verlag]] |location=Berlin, Germany |isbn=3-540-06242-4 |lccn=73-80607 |pages=272–274}}</ref> The quefrency is a measure of time, though not in the sense of a signal in the [[time domain]]. For example, if the sampling rate of an audio signal is 44100&nbsp;Hz and there is a large peak in the cepstrum whose quefrency is 100 samples, the peak indicates the presence of a fundamental frequency that is 44100/100 = 441&nbsp;Hz. This peak occurs in the cepstrum because the harmonics in the spectrum are periodic and the period corresponds to the fundamental frequency, since harmonics are integer multiples of the fundamental frequency.<ref>{{cite web|url=https://support.ircam.fr/docs/AudioSculpt/3.0/co/Discrete%20Cepstrum.html |title=Introduction - Discrete Cepstrum |publisher=Support.ircam.fr |date=1990-01-01 |accessdate=2022-09-16}}</ref>

{{anchor|Kepstrum}}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. It was in use before the cepstrum.<ref>
"Predictive decomposition of time series with applications to seismic exploration", E. A. Robinson MIT report 1954; Geophysics 1967 vol. 32, pp. 418–484;<br/>
"Use of the kepstrum in signal analysis", M. T. Silvia and E. A. Robinson, Geoexploration, volume 16, issues 1–2, April 1978, pages 55–73.
</ref><ref>
"A kepstrum approach to filtering, smoothing and prediction with application to speech enhancement", T. J. Moir and J. F. Barrett, Proc. Royal Society A, vol. 459, 2003, pp. 2957–2976.
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{{anchor|Autocepstrum}} The autocepstrum is defined as the cepstrum of the [[autocorrelation]]. The autocepstrum is more accurate than the cepstrum in the analysis of data with echoes.

{{anchor|Filter|Lifter}}Playing further on the anagram theme, a filter that operates on a cepstrum might be called a ''lifter''. A low-pass lifter is similar to a [[low-pass filter]] in the [[frequency domain]]. It can be implemented by multiplying by a window in the quefrency domain and then converting back to the frequency domain, resulting in a modified signal, i.e. with signal echo being reduced.