genburg.3

speech signal process tools

.\" Copyright (c) 1991 Entropic Research Laboratory, Inc.; All rights reserved
.\" @(#)genburg.3	1.3 06 May 1997 ERL
.ds ]W (c) 1991 Entropic Research Laboratory, Inc.
.TH  GENBURG 3\-ESPSsp 06 May 1997
.SH NAME

.nf
genburg \- generalized Burg (structured covariance) estimation of covariance matrix
.fi
.SH SYNOPSIS
.nf
.ft B
 
#include <esps/stdio.h>
#include <esps/window.h>
#include <esps/ana_methods.h>

extern int debug_level;

genburg(sigma_in, isigma_in, qd, pdist, sigma_out, isigma_out, c_flag, 
	monitor_flag, ret_flag, R_out, iR_out, init_flg, anderson)

double *sigma_in;*
double *isigma_in;*
int    *qd;*
double *pdist;
doulbe *sigma_out;*
doulbe *isigma_out;*
double *R_out;*
double *iR_out;*
int    c_flag;*
int    monitor_flag;*
int    *ret_flag;*
int    init_flg;*
int    anderson;

.ft
.fi
.SH DESCRIPTION
.PP
\fIgenbug\fP uses the algorithms discussed in [1] and [2] to find the
best estimate for the covariance matrix of single channel real or
complex problem.  The input is a Hermitian sample covariance matrix,
and the output is a Hermition (block) Toeplitz matrix.  All matrics
are stored in row order.  Input sample covariance matrices can be
obtained from \fIestimate_covar\fP (3\-\s-1ESPS\s+1sp).
.PP
\fIsigma_in\fP is the address of the real part of the input sample
covariance matrix, and \fIisigma_in\fP is the address of the imaginary
part. \fIqd\fP is the size (1 dimension) of the input (and output)
matrices.
.PP
\fIsigma_out\fP is the address of the real part of the output output
matrix, and \fIisigma_out\fP is the address of the imaginary part. If
\fIinit_flg\fP == 1 (see below), \fIsigma_out\fP and \fIisigma_out\fP
are also as inputs to pass an initial guess to \fIgenburg\fP.
\fIR_out\fP and \fIiR_out\fP are the final solution vectors used to
construct \fIsimga_out\fP and \fIisigma_out\fP.  
The finnal distance or measure is returned via \fIpdist\fP. 
.PP
If \fIc_flag\fP != 0, the inputs are complex.  If \fImonitor_flag\fP
!= 0, intermediate results are printed on stdout.  
.PP
A function return status is returned in \fIret_flag\fP, with 
values as follows (some of these refer to internals of the algorithm): 
.nf

	0 = no decrease in measure after 4 attempts
	1 = Rinit or Rnew is singular or Rinit is negative definite
	2 = sigma_in or Rinit is non-pos-definite 
	3 = Aij singular 
	4 = unsuccessful interpolation, or non positive definite Rnew
	5 = successful measure ratio convergence test 
	6 = insufficient storage allocation

.fi
The parameter \fIinit_flag\fP has the following meanings: 
.nf

	0 = use identity matrix as initial guess 
	1 = use \fIsigma_out\fP and possibly \fIisigma_out\fP as initial guess
	2 = use the first projection of \fIsigma_in\fP as initial guess
	3 = use average + first projection as initial guess


.fi
IF \fIanderson\fP != 0, the Anderson version of the algorithm is used.
Otherwise, the Burg version is used.  
.SH EXAMPLES
.PP
.SH ERRORS AND DIAGNOSTICS
.PP

.SH FUTURE CHANGES
.PP
.SH BUGS
.PP
This function is more general though not as reliable as the function
\fIstruct_cov\fP(3\-\s-1ESPS\s+1sp).
.SH REFERENCES
.TP
[1]
J.P.Burg, D.G.Luenberger, D.L.Wenger, "Estimation of Structured
Covariance Matrices" \fIProceedings of the IEEE\fP, Vol. 70, No. 9
September 1982
.TP
[2] T.W. Anderson, "Estimation for Autoregressive Moving Average
Models in the Timne and Frequency Domain," \fIThe Annals of
Statistics\fP, 1977, Vol. 5, No. 5, 842-865.
.TP
[3]
J.E. Shore, "On a Relation Between Maximum Liklihood Classification 
and Minimum Relative-Entropy Classification, \fIIEEE Transactions on 
Information Theory\fP, Vol. IT-30, No. 6, Nov. 1984, pp. 851-854.
.SH "SEE ALSO"
.PP
.nf
\fIestimate_covar\fP(3\-\s-1ESPS\s+1), \fIget_auto\fP(3\-\s-1ESPS\s+1), 
\fIstrcov_auto\fP(3\-\s-1ESPS\s+1), \fIstruct_cov\fP(3\-\s-1ESPS\s+1),
\fIget_vburg\fP(3\-\s-1ESPS\s+1), \fIrefcof\fP(1\-\s-1ESPS\s+1), 
\fIme_spec\fP(1\-\s-1ESPS\s+1)
.fi
.SH AUTHOR
.PP
Program by Daniel Wenger, minor revisions and man page by John Shore.