computes the power cepstrum of data.


computes the specified type of cepstrum of data.

Details and Options

  • Cepstral analysis has been used for characterization of echoes, separation of convolved signals and pitch detection application in signal processing.
  • Real cepstrum is computed as the inverse Fourier transform of the log-magnitude Fourier spectrum.
  • The data can be any of the following:
  • listarbitrary rank numerical or Quantity array
    audioan Audio or Sound object
    imagearbitrary Image or Image3D object
  • The type specification can be either of the following:
  • "Power"|F^(-1)log(TemplateBox[{{F, (, data, )}}, Abs]^2)|^2
    "Real"TemplateBox[{Re, paclet:ref/Re}, RefLink, BaseStyle -> {2ColumnTableMod}](F^(-1)log(TemplateBox[{{F, (, data, )}}, Abs]))
  • For multichannel images and audio signals, CepstrumArray is returned separately on each channel.
  • CepstrumArray accepts the FourierParameters option. The default setting is FourierParameters->{1,-1}.


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Basic Examples  (2)

Cepstrum of a list:

Cepstrum of an Audio object:

Plot of the power cepstrum:

Scope  (6)

Real cepstrum of a list:

Cepstrum of a 2D list:

Compute the cepstrum of a Sound:

Cepstrum of a multichannel Audio object:

The cepstrum is computed separately on each channel:

Cepstrum of an Image object:

Plot of the power cepstrum:

Cepstrum of a multichannel image:

The cepstrum is computed separately on each channel:

Applications  (3)

Detect the effect of a comb filer on a signal:

The signal only has two sinusoidal components.

A comb filter with delay of 31 samples is applied:

It is not easy to identify the periodicity of the comb filter by using conventional spectral analysis:

Since the cepstrum of a convolution is the sum of the cepstra of the two components, it is easier to identify the peak caused by the comb filter:

Measure the time constant of an echo:

Compute the logarithm of the cepstrum, and discard the second half (the real cepstrum is symmetric):

Find the peaks:

Plot the result:

Select the position of the biggest peak:

Compute the period by dividing the quefrency by the sample rate:

Detect the pitch of a recording:

In harmonic sounds, the pitch does not correspond to the biggest peak in the spectrum:

Compute the cepstrum and discard the symmetric part:

Find the peaks and display the result:

The peak corresponding to zero quefrency is discarded, and the biggest peak is selected:

Compute the fundamental frequency by dividing the sample rate by the quefrency:

Check the result:

Introduced in 2017