Signal Processing Toolbox™

rceps - Real cepstrum and minimum phase reconstruction

Syntax

rceps(x) [y,ym] = rceps(x)

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

Note rceps only works on real data.

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.

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))));

[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.