Construct · 2 fields · 3 citations

cepstrum: one construct, many systems

One name. One construct. Different systems. One map.

● invariant · one method, two disciplines Nearest construct by meaning·not indexed
cepstrum2 SYSTEMSSpeech DSPNOLL · CEPSTRUM PITCHSeismologyULRYCH · HOMOMORPHIC

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1967Speech DSP1971Seismology
2026

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Speech signal processing

the spectrum of the log spectrum, used to find pitch and separate source from filter

The cepstrum is the inverse transform of the logarithm of a signal's spectrum; its independent variable, 'quefrency', has units of time. The term was coined by Bogert, Healy, and Tukey (1963) by anagramming 'spectrum', and Noll (1967) used cepstrum pitch determination to find the fundamental of speech; Oppenheim and Schafer (2004) trace its history. The same operation recurs in seismology; it is genuinely one construct, not a coincidence of spelling.[1][2]

Unit
One cepstrum (amplitude vs. quefrency)
Recovery means
Take the inverse transform of the log-magnitude spectrum and read peaks in quefrency.
Measured by
FFT → log magnitude → inverse FFT; a peak at quefrency 1/f0 marks the pitch period.

Seismology

cepstral (homomorphic) analysis to detect and remove seismic echoes

In seismology the cepstrum is used for homomorphic deconvolution: separating a seismic wavelet from the earth's reflectivity and detecting echoes. Ulrych (1971), in Geophysics, applied homomorphic (cepstral) deconvolution to seismograms. The mathematics is identical to the speech cepstrum, applied to ground motion instead of the voice, which makes the two an invariant rather than a jingle.[3]

Unit
One cepstrum of a seismic trace
Recovery means
Compute the cepstrum of a seismogram and identify quefrency peaks from echo delays.
Measured by
Homomorphic deconvolution: log-spectral liftering to isolate the wavelet from reflectivity.

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Nearby constructs

construct6 fields · 7 citationsjingle · one name, six constructsdetermination1 fields · 1 citationsanchor · a standalone constructground4 fields · 7 citationsjingle · one word, four constructs

References

  1. Noll, A. M. (1967). Cepstrum pitch determination. The Journal of the Acoustical Society of America, 41(2), 293–309. https://doi.org/10.1121/1.1910339
  2. Oppenheim, A. V., & Schafer, R. W. (2004). From frequency to quefrency: A history of the cepstrum. IEEE Signal Processing Magazine, 21(5), 95–106. https://doi.org/10.1109/MSP.2004.1328092
  3. Ulrych, T. J. (1971). Application of homomorphic deconvolution to seismology. Geophysics, 36(4), 650–660. https://doi.org/10.1190/1.1440202

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