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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. |
References
[1] Oppenheim, A.V., and R.W. Schafer. Digital Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1975. [2] IEEE. Programs for Digital Signal Processing. IEEE Press. New York: John Wiley & Sons, 1979.