A cepstrum is a time history defined as the power spectrum of the logarithm of the Power spectrum. This, you can interpret as the spectrum of a spectrum. It extracts periodicities in the spectrum, such as harmonic families and sidebands. The imaginary part is the Hilbert transform.

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 autocorrelation function.

  • Gearbox analysis
  • Bearing analysis

The cepstrum also has weighting functions, called lifters. The purpose of the lifters is to eliminate a part of the information in the cepstrum before the transformation. For instance, the comb lifter can remove a whole harmonic family.

Application examples:
  • Echo removal
  • Speech analysis
  • Gearbox analysis
  • Bearing analysis

See also: Autocorrelation, Echo, Echo Location.

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Subjects: Noise & Vibration Signal Processing