Definitions of CEPSTRUM ( a re-attangement / anagram of the letters of spectrum / spelled as septrum earlier )

return to Breakthru in Measuring INTERNAL COHERENCE.Teaching Biological Oscillators SUSTAINABILITY -

(note -- it appears particularly that the lower frequency bandwidth within which the significant power densitites of the EKG exist - allow the cepstrum technique - to qunatify internal coherence - specifically quantizing the onset of phase synchrony between internal harmonic constituents.)

per National Instruments:

Cepstrum Definition:

The Fourier transform of the logarithm of the autospectrum. Useful for determining periodicities in the autospectrum. Additions in the cepstrum domain correspond to multiplication in the frequency domain and convolution in the time domain.

V or dB vs. s



The cepstrum is the forward Fourier transform of a spectrum. It is thus the spectrum of a spectrum, and has certain properties that make it useful in many types of signal analysis. One of its more powerful attributes is the fact that any periodicities, or repeated patterns, in a spectrum will be sensed as one or two specific components in the cepstrum. If a spectrum contains several sets of sidebands or harmonic series, they can be confusing because of overlap. But in the cepstrum, they will be separated in a way similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes and rolling element bearing vibrations lend themselves especially well to cepstrum analysis. The cepstrum is closely related to the auto correlation function.

from - about Cepstrum

1. The term cepstrum was introduced by Bogert et al. and has come to be accepted terminology for the (note insert from dan winter - this is wrong! it is not inverse) inverse Fourier transform of the logarithm of the power spectrum of a signal. (L.R.Rabiner and R.W.Schafer, Digital Processing of Speech Signals, Prentice Hall, Englewood Cliffs, NJ, 1978)

2. In 1963, Bogert, Healy and Tukey published a paper with the unusual title "The Quefrency Analysis of Time Series for Echoes: Cepstrum, Pseudoautocovariance, Cross-Cepstrum, and Saphe Cracking."
They observed that the logarithm of the power spectrum of a signal containing an echo has an additive periodic component due to the echo, and thus the Fourier transform of the logarithm of the power spectrum should exhibit a peak at the echo delay. They called this function the cepstrum, interchanging letters in the word spectrum because "in general, we find ourselves operating on the frequency side in ways customary on the time side and vice versa."
Bogert et al. went on to define an extensive vocabulary to describe this new signal processing technique; however, only the term cepstrum has been widely used. (A.V.Oppenheim and R.W.Schafer, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1989)

3. The transformation of a signal into its cepstrum is a homomorphic transformation, and the concept of the cepstrum is a fundamental part of the theory of homomorphic systems for processing signals that have been combined by convolution. (A.V.Oppenheim and R.W.Schafer, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1989)

4. Books including the subject about cepstrum and homomorphic systems
* Discrete-Time Signal Processing, A.V.Oppenheim and R.W.Schafer, Prentice Hall
* Digital Processing of Speech Signals, L.R.Rabiner and R.W.Schafer, Prentice Hall
* Discrete-Time Processing of Speech Signals, J.R.Deller,Jr., J.G.Proakis and J.H.L.Hansen, Prentice Hall
* Seismic Applications of Homomorphic Signal Processing, J.M.Tribolet, Prentice Hall

* Onsei Singou Syori (in Japansese, Speech Signal Processing), S.Imai, Morikita Publishing

This book describes modern Cepstrum analysis technology and its applications in speech processing.
For example,
 log magnitude approximation (MLA)
6. Example of the Hypersigal worksheet of power cepstrum-source of Hypersignal worksheet

7. Cepstrum Co., Ltd. is a developer of digital signal processing system/software in Japan.
Also Cepstrum is the dealer and 3rd party developer of Hypersignal in Japan.