fftcep.1

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.\" Copyright (c) 1990 Entropic Speech, Inc.
.\" Copyright (c) 1996 Entropic Research Laboratory, Inc. All rights reserved.
.\" @(#)fftcep.1	1.5 01 Oct 1998 ESI/ERL
.ds ]W (c) 1993 Entropic Research Laboratory, Inc.
.TH FFTCEP 1\-ESPS 01 Oct 1998
.SH "NAME"
fftcep \- FFT-based complex cepstrum of ESPS sampled data 

.SH "SYNOPSIS"
.B fftcep 
[
.BI \-P " param"
] [
.BI \-r " range"
] [ 
.BI \-l " frame_len"
] [
.BI \-S " step"
] [
.BI \-w " window_type"
] [
.BI \-o " order"
] [
.BI \-F
] [
.BI \-R
] [
.BI \-e " element_range"
][
.BI \-z " zeroing_range"
][
.BI \-x " debug_level"
] 
.I sd_file 
.I fea_file

.SH "DESCRIPTION"
.PP
.I fftcep 
takes an input ESPS sampled data (SD or FEA_SD) file,
\fIsd_file\fP, and finds the complex cepstrum of one or more fixed length
segments to produce an ESPS FEA file, 
.I fea_file.  
If the input file name 
.I sd_file
is replaced by "\-", stdin is read; similarly, if 
.I fea_file
is replaced by "\-", the output is written to stdout.
The \fIFEA_SD\fP(5\-\s-1ESPS\s+1) files support complex
sampled data, and \fIfftcep\fP will process complex input data,
as well as multichannel data.
.PP
The complex cepstrum of a single frame is computed by obtaining the
FFT of the (possibly windowed) data frame, computing the complex
logarithm of this spectrum, and finding the inverse FFT of the log
spectral data. The complex cepstrum of single channel input 
is stored in the field \fIcepstrum_0\fP whose default data type 
is FLOAT_CPLX.  If the input has \fIN\fP channels, the cepstral
data corresponding to the \fPith\fP channel is stored in field
\fIcepstrum_i\fP, where 0 <= \fIi\fP < \fIN\fP; the data in each
channel is processed identically.
.PP
The \fB\-R\fP option specifies that the cepstrum rather than the complex
cepstrum should be computed. In this case, the inverse FFT is performed on
the log magnitude of the spectrum, rather than on the complex
logarithm of the spectrum. Under the \fB\-R\fP option, the cepstrum of
single channel data 
is stored in the field \fIcepstrum_0\fP and its default data 
type is FLOAT_CPLX. Field names for multichannel data are constructed
as in the complex cepstrum case, and the data in each channel
is processed identically.
.PP
When computing either the cepstrum or complex cepstrum, the 
option \fB\-F\fP specifies that the imaginary
part of the resulting data be discarded and only the real part be stored; 
the field \fIcepstrum_0\fP then has type FLOAT.
.PP
All input frames have the same length
.I frame_len
(see the \fB\-l\fP option).  The
initial point of the first frame is determined by the \fB\-r\fP option or by
.I start
in the parameter file.  Initial points of subsequent frames 
follow at equal interval 
.I step
(see \fB\-S\fP option).  Thus the 3 cases 
.I step 
< 
.I frame_len, 
.I step 
= 
.I frame_len, 
.I step 
> 
.I frame_len, 
correspond 
to overlapping frames, exactly abutted frames, and frames separated by
gaps.
.PP
The number of frames is the minimum sufficient to cover a specified range of
.I nan
points (see \fB\-r\fP option), given 
.I frame_len 
and 
.I step.  
The last frame may
overrun the range, in which case a warning is issued.  If a frame overruns
the end of the input file, it is filled out with zeros.
.PP
The FFT cepstral routines used by \fIfftcep\fP return
2^\fIorder\fP values (see \fIfft_cepstrum\fP(3\-\s-1ESPS\s+1)).  The default
is always to store all 2^\fIorder\fP values in \fIcepstrum_0\fP in the same order 
as returned by \fIget_cfft_inv\fP(3-ESPS); the cepstral sequence is
returned in the following order:
c(0), c(1),..., c(N/2), c(-(N/2) + 1), c(-(N/2) + 2),..., c(-1).
It is possible to specify that a subrange of these values
be used to form \fIcepstrum_0\fP (see \fB\-e\fP option).
This makes it possible to discard cepstral information not relevant
to further processing.  
.PP
It is possible to perform simple filtering on the cepstral data.
The \fB\-z\fP option can be used to set elements of the cepstral data to zero. To 
apply more complicated operations to the cepstral data, \fBfeafunc\fP(1-ESPS) can be
used to process the field \fIcepstrum_0\fP directly and 
\fBmake_sd\fP(1-ESPS) can be used to 
create \fIFEA_SD\fP(5-ESPS) 
files which can be processed with \fBwindow\fP (1-ESPS).
.PP
\fBExample Shell Script\fP
.br
The following shell script is an example of using \fIfftcep\fP
to analyze a segment of speech.  The FFT spectrum as found by
\fIfft\fP(1\-\s-1ESPS\s+1) can be compared to the spectrum
of the liftered cepstral sequence 
computed by \fIfftcep\fP.  A 512 point segment is read from the
file \fI/usr/esps/demo/speech.sd\fP by \fIfft\fP and \fIfftcep\fP.
Both programs compute a 1024 point FFT from the Hamming windowed
sequence, and \fIfftcep\fP is forced to compute and store the real
part of the power cepstrum.  Liftering is performed by using the
\fB\-z\fP option to set the long-time cepstral components to zero.
The program \fImake_sd\fP(1\-\s-1ESPS\s+1) must be used to translate
the FEA file output of \fIfftcep\fP into the FEA_SD file format
expected by \fIfft\fP.
The program \fIplotspec\fP(1\-\s-1ESPS\s+1) can be used to compare
the FFT spectrum with the spectrum of the liftered cepstral sequence.
.PP
#!/bin/csh
.br
set spfile = /usr/esps/demo/speech.sd
.br
set sf = `hditem -i record_freq $spfile`
.br
#
.br
fft -r1000:1511 -o10 -l512 -wHAMMING $spfile speech.spec 
.br
plotspec -p0:4000 speech.spec
.br
#
.br
fftcep -r1000:1511 -o10 -l512 -wHAMMING -F -R -z23:1000 \\
.br
	$spfile speech.cep 
.br
make_sd -r1: -fcepstrum_0 -S$sf speech.cep speech.cepsd
.br
fft -p1:3072 -o10 -l1024 speech.cepsd speech.cspec
.br
plotspec -p0:4000 speech.cspec
.PP

.SH "OPTIONS"
.PP
The following options are supported:
.TP
.BI \-P " param"
uses the parameter file 
.I param
rather than the default, which is
.I params.
.TP
.BI \-r " first" : "last"
.TP
.BI \-r " first" \- "last"
.TP
.BI \-r " first" :+ "incr"
In the first two forms, a pair of unsigned integers specifies the range of
sampled data to analyze.  If 
.IR last " = " first " + " incr,
the third form (with the plus sign) specifies the same range as the
first two forms.  If 
.I first
is omitted, the default value of 1 is used.  If
.I last
is omitted, the range extends to the end of the file.
If the specified range extends beyond the end of the file,
it is reduced to end at the end of the file.
Then, if the range doesn't end on a frame boundary,
it is extend to make up a full last frame.
If the range, so extended, goes past the end of the file,
the last frame is filled out with zeros.
All forms of the option override the values of 
.I start
and
.I nan
in the parameter file or ESPS Common file.
The first two forms are equivalent to supplying values of
.I first
for the parameter
.I start
and
.RI ( last " + 1 \- " first )
for the parameter
.I nan.
The third form is equivalent to values of
.I first
for
.I start
and
.RI ( incr " + 1)"
for
.I nan.
If the \fB\-r\fP option is not
used, the range is determined from the ESPS Parameter or Common file if the
appropriate parameters are present.
.TP
.BI \-l " frame_len" "\fR [0]"
Specifies the length of each frame.
If the option is omitted, the parameter file is consulted.
A value of 0 (from either the option or the parameter file)
indicates that a default value is to be used:
the transform length determined by the order.  (See the
.B \-o
option and the
.I order
parameter.)
This is also the default value in case
.I frame_len
is not specified either with the
.B \-l
option or in the parameter file.
.TP
.BI \-S " step" "\fR [" frame_len "\fR]"
Initial points of consecutive frames differ by this number of samples.
If the option is omitted, the parameter file is consulted,
and if no value is found there, a default equal to
.I frame_len
is used (resulting in exactly abutted frames).
The same default applies if \fIstep\fP is given a value of 0.
.TP
.BI \-w " window_type" " \fR[RECT]"
The name of the data window to apply to the data in each frame before
computing the FFT.  If the option is omitted, the parameter
file is consulted, and if no value is found there, the default used is a
rectangular window with amplitude one.  Possible window types include
rectangular ("RECT"), Hamming ("HAMMING"), Hanning ("HANNING"),
cos^4 ("COS4"), and triangular ("TRIANG"); see
the window (3-ESPS) manual page for the complete list.
.TP
.BI \-o " order" "\fR [10]\fP"
The order of the FFT and inverse FFT; the transform length is 2^\fIorder\fP
(2 to the \fIorder\fP-th 
power).  If the number of data points in each frame (frame length) is less
than the transform length, the frame is padded with zeros (a warning is
given).  If the number of data points in each frame exceeds the transform
length, only the first 2^\fIorder\fP points from each frame are 
transformed \-
i.e., points are effectively skipped between each transform (a warning is
given).  The default order is 10 (transform length 1024).