'\" te
.\" Copyright (c) 2007, Sun Microsystems, Inc.  All Rights Reserved 
.TH mlib_SignalLPCCovariance_F32 3MLIB "2 Mar 2007" "SunOS 5.11" "mediaLib Library Functions"
.SH NAME
mlib_SignalLPCCovariance_F32 \- perform linear predictive coding with covariance method
.SH SYNOPSIS
.LP
.nf
cc [ \fIflag\fR... ] \fIfile\fR... \fB-lmlib\fR [ \fIlibrary\fR... ]
#include <mlib.h>

\fBmlib_status\fR \fBmlib_SignalLPCCovariance_F32\fR(\fBmlib_f32 *\fR\fIcoeff\fR,
     \fBconst mlib_f32 *\fR\fIsignal\fR, \fBvoid *\fR\fIstate\fR);
.fi

.SH DESCRIPTION
.sp
.LP
The \fBmlib_SignalLPCCovariance_F32()\fR function performs linear predictive coding with covariance method.
.sp
.LP
In linear predictive coding (LPC) model, each speech sample is represented as a linear combination of the past \fBM\fR samples.
.sp
.in +2
.nf
	        M
	s(n) = SUM a(i) * s(n-i) + G * u(n)
	       i=1
.fi
.in -2

.sp
.LP
where \fBs(*)\fR is the speech signal, \fBu(*)\fR is the excitation signal, and \fBG\fR is the gain constants, \fBM\fR is the order of the linear prediction filter. Given \fBs(*)\fR, the goal is to find a set of coefficient \fBa(*)\fR that minimizes the prediction error \fBe(*)\fR.
.sp
.in +2
.nf
	               M
	e(n) = s(n) - SUM a(i) * s(n-i)
	              i=1
.fi
.in -2

.sp
.LP
In covariance method, the coefficients can be obtained by solving following set of linear equations.
.sp
.in +2
.nf
	 M
	SUM a(i) * c(i,k) = c(0,k), k=1,...,M
	i=1
.fi
.in -2

.sp
.LP
where
.sp
.in +2
.nf
	         N-k-1
	c(i,k) =  SUM s(j) * s(j+k-i)
	          j=0
.fi
.in -2

.sp
.LP
are the covariance coefficients of \fBs(*)\fR, \fBN\fR is the length of the input speech vector.
.sp
.LP
Note that the covariance matrix \fBR\fR is a symmetric matrix, and the equations can be solved efficiently with Cholesky decomposition method.
.sp
.LP
See \fIFundamentals of Speech Recognition\fR by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.
.SH PARAMETERS
.sp
.LP
The function takes the following arguments:
.sp
.ne 2
.mk
.na
\fB\fIcoeff\fR\fR
.ad
.RS 10n
.rt  
The linear prediction coefficients.
.RE

.sp
.ne 2
.mk
.na
\fB\fIsignal\fR\fR
.ad
.RS 10n
.rt  
The input signal vector.
.RE

.sp
.ne 2
.mk
.na
\fB\fIstate\fR\fR
.ad
.RS 10n
.rt  
Pointer to the internal state structure.
.RE

.SH RETURN VALUES
.sp
.LP
The function returns \fBMLIB_SUCCESS\fR if successful. Otherwise it returns \fBMLIB_FAILURE\fR.
.SH ATTRIBUTES
.sp
.LP
See \fBattributes\fR(5) for descriptions of the following attributes:
.sp

.sp
.TS
tab() box;
cw(2.75i) |cw(2.75i) 
lw(2.75i) |lw(2.75i) 
.
ATTRIBUTE TYPEATTRIBUTE VALUE
_
Interface StabilityCommitted
_
MT-LevelMT-Safe
.TE

.SH SEE ALSO
.sp
.LP
\fBmlib_SignalLPCCovarianceInit_F32\fR(3MLIB), \fBmlib_SignalLPCCovarianceFree_F32\fR(3MLIB), \fBattributes\fR(5)