Signal Processing Toolbox

cceps

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 is an M-file implementation of algorithm 7.1 in [2]. A lengthy Fortran program reduces to these three lines of MATLAB code, which compose the core of cceps:

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

Note    rcunwrap in the above code segment is a special version of unwrap that subtracts a straight line from the phase. rcunwrap is a local function within cceps and is not available for use from the MATLAB command line.

See Also

icceps, hilbert, rceps, unwrap

References

[1] Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 788-789.

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

buttord

cell2sos