rceps (Signal Processing Toolbox)

Real cepstrum and minimum phase reconstruction.

Syntax

y = rceps(x)
[y,ym] = rceps(x)

Description

The real cepstrum is the inverse Fourier transform of the real logarithm of the magnitude of the Fourier transform of a sequence.

rceps(x) returns the real cepstrum of the real sequence x. The real cepstrum is a real-valued function.

[y,ym] = rceps(x) returns both the real cepstrum y and a minimum phase reconstructed version ym of the input sequence.

Algorithm

rceps is an M-file implementation of algorithm 7.2 in [2], that is,

y = real(ifft(log(abs(fft(x)))));

Appropriate windowing in the cepstral domain forms the reconstructed minimum phase signal.

w = [1; 2*ones(n/2-1,1); ones(1 - rem(n,2),1); zeros(n/2-1,1)];
ym = real(ifft(exp(fft(w.*y))));

See Also

cceps
Complex cepstral analysis.

fft
One-dimensional fast Fourier transform.

hilbert
Hilbert transform.

icceps
Inverse complex cepstrum.

unwrap
Unwrap phase angles.

`cceps`	Complex cepstral analysis.
`fft`	One-dimensional fast Fourier transform.
`hilbert`	Hilbert transform.
`icceps`	Inverse complex cepstrum.
`unwrap`	Unwrap phase angles.

References

[1] Oppenheim, A.V., and R.W. Schafer, Digital Signal Processing, Englewood Cliffs, NJ, Prentice-Hall, 1975.

[2] Programs for Digital Signal Processing, IEEE Press, New York, 1979.

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