toep_solv.1

speech signal process tools

.\" Copyright (c) 1986-1990 Entropic Speech, Inc.
.\" Copyright (c) 1992 Entropic Research Laboratory, Inc.  All rights reserved.
.\" @(#)toep_solv.1	1.3 12/2/92 ESI/ERL
.ds ]W (c) 1992 Entropic Research Laboratory, Inc.
.if n \{\
. ds R_ \x'1'R\d\dij\u\u
. ds r_ \x'1'r\d\d|i-j|\u\u
. ds r0 \x'1'r\d\d0\u\u
. ds r1 \x'1'r\d\d1\u\u
. ds rm \x'1'r\d\dm\u\u
. \}
.if t \{\
. ds R_ \fIR\v'15u'\s-3i\^j\s+3\|\v'-15u'\fP
. ds r_ \fIr\fP\v'15u'\s-3|\|\fIi\|\(mi\^j\fP\^|\s+3\v'-15u'
. ds r0 \fIr\fP\v'15u'\s-3\fR0\fP\s+3\v'-15u'
. ds r1 \fIr\fP\v'15u'\s-3\fR1\fP\s+3\v'-15u'
. ds rm \fIr\v'15u'\s-3m\s+3\v'-15u'\fP
. \}
.TH TOEP_SOLV 1\-ESPS 12/2/92
.SH "NAME"
toep_solv \- Solve real symmetric Toeplitz systems of linear equations
.SH "SYNOPSIS"
.B toep_solv
[
.BI \-f " crsfield"
] [
.BI \-x " debug_level"
] [
.BI \-F " autfield"
] [
.BI \-P " param"
] [
.BI \-W " pwrfield"
]
.I autocor.fea
.I crosscor.fea
.I output.filt
.SH "DESCRIPTION"
.PP
.I Toep_solv
repeatedly obtains an ``autocorrelation vector''
.I r
from its first input file
and a corresponding ``cross-correlation vector''
.I v
from its second file.
For each such pair of vectors, it solves the system of equations
.PP
.I Rw = v
.PP
where
.I R
is a Toeplitz matrix with coefficients given by
.PP
\*(R_\ =\ \*(r_
.PP
and writes the solution vector
.I w
to the output file.
.PP
The first input file is typically a FEA_ANA file
containing normalized autocorrelations,
as indicated by a value AUTO for the header item
.I spec_rep
(see FEA_ANA(5\-ESPS)).
However, any FEA file having a scalar field
.I raw_power
and a vector field
.I spec_param
of type FLOAT is accepted,
and in fact alternative field names may be chosen
with the
.B \-W
and
.B \-F
options.
A vector
.I r
is obtained from these two fields in each input record.
The value of \*(r0 is the contents of the
.I raw_power
field,
and the values of \*(r1,\ .\ .\ .\ ,\ \*(rm
are obtained by multiplying the contents of the
.I spec_param
field by \*(r0.
Here
.I m,
the size of the
.I spec_param
field, equals the order of the autocorrelations.
.PP
The second input file may be any FEA file having a vector field
.I cross_cor
of type FLOAT, and an alternative field name may be chosen
with the
.B \-f
option.
For example files written by the program
.IR cross_cor (1\-ESPS)
are acceptable.
The vector
.I v
obtained from each record is simply the contents of the given field.
The size of the field must be
.IR m "\|+\|1,"
where
.I m,
as above, is the size of the
.I spec_param
field in the first input file.
.PP
The output file is a FEA_FILT file.
The elements of each solution vector
.I w
are treated as coefficients of a FIR filter and written in an output
record as elements of 
.I re_num_coeff.
.PP
The solution vectors are computed by
.IR stsolv (3-ESPS),
which uses Levinson's method \-
reflection coefficients are computed as intermediate results,
and a warning is printed
if a reflection coefficient with magnitude 1 or greater is computed.
In that case
the output record contains the solution of a system of some reduced order.
.SH "OPTIONS"
.PP
The following options are supported.  Default values are shown in brackets.
.TP
.BI \-f " crsfield" " \fR[cross_cor]"
The name of the field in the second input file that contains the
cross-correlation vectors
.I v.
.TP
.BI \-x " debug_level" " \fR[0]"
A positive value causes various debugging messages to be printed to the
standard error output \- the higher the value, the more messages.
At the default level of 0, no messages are printed.
.TP
.BI \-F " autfield" " \fR[spec_param]"
The name of the field in the first input file that contains the normalized
autocorrelation vectors used in computing the autocorrelation vectors
.I r.
.TP
.BI \-P " param" " \fR[params]"
.TP
.BI \-W " pwrfield" " \fR[raw_power]"
The name of the field in the first input file
that contains the total power \*(r0
used in computing the autocorrelation vectors
.I r.
.SH "ESPS PARAMETERS"
.PP
The parameter file does not have to be present,
since all the parameters have default values.
The following parameters are read, if present, from the parameter file:
.TP
.I "crsfield \- string"
The name of the field in the second input file
that contains the cross-correlation vectors.
This parameter is not read if the
.B \-f
option is used.
The default is "cross_cor".
.TP
.I "autfield \- string"
The name of the field in the first input file
that contains the normalized autocorrelation vectors.
This parameter is not read if the
.B \-F
option is used.
The default is "spec_param".
.TP
.I "pwrfield \- string"
The name of the field in the first input file
that contains the total power.
This parameter is not read if the
.B \-W
option is used.
The default is "raw_power".
.SH "ESPS COMMON"
The ESPS common file is not accessed.
.SH "ESPS HEADERS"
The value of
.I common.type
is checked in the two input file headers.
The output header is a new FEA_FILT file header.
The generic header item 
.I max_num
is set equal to the number of output filter coefficients,
which is the same as the number of elements
of an input cross-correlation vector;
.I max_denom
becomes 0.
The values given to
.I type
and
.I method
are FILT_ARB and PZ_PLACE.
All other FEA_FILT generic header items are filled in with
NONE, 0, or NULL.
Generic header items
.I crsfield, autfield,
and
.I pwrfield
are added to record the values obtained from the command line,
from the parameter file, or by default.
As usual, the command line is added as a comment, and the headers of the
input files are added to the output file header as source files.
.SH "EXAMPLE"
.PP
Sometimes one needs to estimate the coefficients of a linear filter,
give two pieces of information:
an original version of a signal
and the corresponding filtered version, possibly with added noise.
An estimate may be obtained as the solution
.I w
of a Toeplitz system for which the matrix elements \*(r_
are autocorrelations of the original signal,
and the right-hand side
.I v
consists of cross-correlations of the filtered signal with the original.
The problem can thus be solved by
.I toep_solv
together with
.IR auto (1-ESPS)
and
.IR cross_cor (1-ESPS).
Suppose for example that the original signal is a thousand-sample segment
of a sampled-data file
.I orig.sd
starting at sample 1001,
and that the filtered signal is in a sampled-data file
.I filt.sd
starting at sample 501.
The following commands will estimate an order-10 causal FIR filter
that will transform the original signal to one as close as possible to
the filtered signal in a least-squares sense.
.nf
.IP
auto \-p1001:2000 \-o10 orig.sd auto.fana
cross_cor \-p501:1500 \-p1001:2000 \-o0:10 filt.sd orig.sd ccor.fea
toep_solv auto.fana ccor.fea filter.filt
.fi

.SH "SEE ALSO"
.PP
stsolv(3-ESPSsp), auto(1-ESPS), cross_cor(1-ESPS), FEA(5-ESPS), FEA_ANA(5-ESPS),
FEA_FILT(5-ESPS)
.SH "BUGS"
.PP
There should be an option \-r to allow selecting a subrange of the records in
the input files.  Tags are ignored.
.SH "FUTURE CHANGES"
.PP
Accommodate double-precision data.
.SH "AUTHOR"
Rodney Johnson. Modified to write FEA_FILT files by Bill Byrne.