fftcepstru.3

speech signal process tools

.\" Copyright (c) 1990 Entropic Speech, Inc.
.\" Copyright (c) 1990-1994 Entropic Research Laboratory, Inc.; All rights reserved.
.\" @(#)fftcepstru.3	1.3 06 May 1997 ESI/ERL
.ds ]W (c) 1993 Entropic Research Laboratory, Inc.
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.if t .ds - \(em\h'-0.5m'\(em
.TH FFT_CEPSTRUM 3\-ESPSsp 3/13/90
.SH NAME
.nf
fft_cepstrum \- Find the cepstrum of a data sequence.
fft_cepstrum_r \- Find the cepstrum of real data sequence.
fft_ccepstrum \- Find the complex cepstrum of a data sequence.
fft_ccepstrum_r \- Find the complex cepstrum of a real data sequence.
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.SH SYNOPSIS
.nf
.ft B
extern int debug_level;

void
fft_cepstrum(data, order)
float_cplx *data;
long order;

void
fft_cepstrum_r(data_real, data_imag, order)
float *data_real, *data_imag;
long order;

void
extern int debug_level;
fft_ccepstrum(data, order)
float_cplx *data;
long order;

void
extern int debug_level;
fft_ccepstrum_r(data_real, data_imag, order)
float *data_real, *data_imag;
long order;
.fi
.SH DESCRIPTION
The \fIfft_cepstrum\fP and \fIfft_ccepstrum\fP routines compute the
cepstrum and complex cepstrum, respectively, of a complex data
sequence using fast Fourier transform
techniques.  The input data is supplied through the array
\fIdata\fP of size 2^\fIorder\fP. The cepstral
data is returned through this array.
.PP
The routine \fIfft_ccepstrum\fP first computes the input spectrum from
\fIdata\fP by using \fIget_cfft\fP(3-ESPS).
The complex logarithm of
this spectrum is then found as described in [1,2].  The inverse
FFT of this log spectral data is found by using
\fIget_cfft_inv\fP(3-ESPS) 
and returned through \fIdata\fP.
The routine \fIfft_cepstrum\fP works identically except that the log magnitude
of the input spectrum is found rather than the complex logarithm.
.PP
The functions \fIfft_cepstrum_r\fP and \fIfft_ccepstrum_r\fP
are identical to \fIfft_cepstrum\fP and \fIfft_ccepstrum\fP except that
they process only real data sequences. They
use \fIget_rfft\fP (3-ESPS) instead of \fIget_fft\fP,
and so are faster than \fIfft_cepstrum\fP and \fIfft_ccepstrum\fP.
The array \fIdata_imag\fP must be filled with zeros when
\fIfft_cepstrum_r\fP and \fIfft_ccepstrum_r\fP are called.
The real and imaginary parts of the result are returned through
\fIdata_real\fP and \fIdata_imag\fP.
.SH SEE ALSO
.IR get_cfft (3-ESPS)
.IR get_cfft_inv (3-ESPS)
.IR get_rfft (3-ESPS)
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.SH COMMENTS
The routine used to compute the complex logarithm attempts to smooth
the phase angle of the spectrum by adding or subtracting 2*pi to phase
values which differ by more than pi from their predecessors.
An additional, linear term is added to the phase to insure that the
phase varies smoothly when continued as a periodic function\*-that is,
that the first and last phase values differ by less than pi\*-and,
in the case of \fIfft_ccepstrum_r\fP, that the result is real.
In terms of the original data, this linear phase shift amounts to a
circular shift of the input array and,
in the case of \fIfft_ccepstrum_r\fP, a possible sign inverison.
In order for this phase unwrapping to succeed,
the phase needs to be slowly varying, which can be achieved by
increasing \fIorder\fP.  If \fIdebug_level\fP is greater than 0, the
unwrapping algorithm checks that unwrapped phase satisfies the
continuity criterion. The warning "Phase unwrapping failed." is echoed
to standard output the first time the criterion is violated.
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.SH REFERENCES
[1] A. V. Oppenheim and R. W. Schafer,
.I Digital Signal Processing
Prentice-Hall, N.J. 1975
.sp
[2] D. G. Childers, D. P. Skinner, R. C. Kemerait,
.I The Cepstrum: A Guide to Processing
Proceedings of the I.E.E.E., vol. 65, no. 10 October 1977, pp. 1428-1443
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.SH AUTHOR
Program and manual page by Bill Byrne.