cceps (Signal Processing Toolbox)

Complex cepstral analysis.

Syntax

xhat = cceps(x)
[xhat,nd] = cceps(x)
[xhat,nd,xhat1] = cceps(x)
[...] = cceps(x,n)

Description

Cepstral analysis is a nonlinear signal processing technique that is applied most commonly in speech processing and homomorphic filtering [1].

xhat = cceps(x) returns the complex cepstrum of the (assumed real) sequence x. The input is altered, by the application of a linear phase term, to have no phase discontinuity at ± radians. That is, it is circularly shifted (after zero padding) by some samples, if necessary, to have zero phase at radians.

[xhat,nd] = cceps(x) returns the number of samples nd of (circular) delay added to x prior to finding the complex cepstrum.

[xhat,nd,xhat1] = cceps(x) returns a second complex cepstrum, computed using an alternate rooting algorithm, in xhat1. The alternate method ([1] p.795) is useful for short sequences that can be rooted and do not have zeros on the unit circle. For these signals, xhat1 can provide a verification of xhat.

[...] = cceps(x,n) zero pads x to length n and returns the length n complex cepstrum of x.

Algorithm

cceps, in its basic form, is an M-file implementation of algorithm 7.1 in [2]. A lengthy Fortran program reduces to three lines of MATLAB code:

h = fft(x);
logh = log(abs(h)) + sqrt(-1)*rcunwrap(angle(h));
y = real(ifft(logh));

rcunwrap is a special version of unwrap that subtracts a straight line from the phase.

See Also

icceps
Inverse complex cepstrum.

hilbert
Hilbert transform.

rceps
Real cepstrum and minimum phase reconstruction.

unwrap
Unwrap phase angles.

`icceps`	Inverse complex cepstrum.
`hilbert`	Hilbert transform.
`rceps`	Real cepstrum and minimum phase reconstruction.
`unwrap`	Unwrap phase angles.

References

[1] Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.

[2] IEEE. Programs for Digital Signal Processing. IEEE Press. New York: John Wiley & Sons, 1979.

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