'\" te
.\" Copyright (c) 2007, Sun Microsystems, Inc.  All Rights Reserved 
.TH mlib_SignalLPCAutoCorrelGetPARCOR_S16 3MLIB "2 Mar 2007" "SunOS 5.11" "mediaLib Library Functions"
.SH NAME
mlib_SignalLPCAutoCorrelGetPARCOR_S16, mlib_SignalLPCAutoCorrelGetPARCOR_S16_Adp \- return the partial correlation (PARCOR) coefficients
.SH SYNOPSIS
.LP
.nf
cc [ \fIflag\fR... ] \fIfile\fR... \fB-lmlib\fR [ \fIlibrary\fR... ]
#include <mlib.h>

\fBmlib_status\fR \fBmlib_SignalLPCAutoCorrelGetPARCOR_S16\fR(
     \fBmlib_s16 *\fR\fIparcor\fR, \fBmlib_s32\fR \fIpscale\fR, \fBvoid *\fR\fIstate\fR);
.fi

.LP
.nf
\fBmlib_status\fR \fBmlib_SignalLPCAutoCorrelGetPARCOR_S16_Adp\fR(
     \fBmlib_s16 *\fR\fIparcor\fR, \fBmlib_s32 *\fR\fIpscale\fR, \fBvoid *\fR\fIstate\fR);
.fi

.SH DESCRIPTION
.sp
.LP
Each of the functions returns the partial correlation (PARCOR) coefficients.
.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 autocorrelation method, the coefficients can be obtained by solving following set of linear equations.
.sp
.in +2
.nf
	 M
	SUM a(i) * r(|i-k|) = r(k), k=1,...,M
	i=1
.fi
.in -2

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

.sp
.LP
are the autocorrelation coefficients of \fBs(*)\fR, \fBN\fR is the length of the input speech vector. \fBr(0)\fR is the energy of the speech signal.
.sp
.LP
Note that the autocorrelation matrix \fBR\fR is a Toeplitz matrix (symmetric with all diagonal elements equal), and the equations can be solved efficiently with Levinson-Durbin algorithm.
.sp
.LP
See \fIFundamentals of Speech Recognition\fR by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.
.sp
.LP
Note for functions with adaptive scaling (with \fB_Adp\fR postfix), the scaling factor of the output data will be calculated based on the actual data; for functions with non-adaptive scaling (without \fB_Adp\fR postfix), the user supplied scaling factor will be used and the output will be saturated if necessary.
.SH PARAMETERS
.sp
.LP
Each function takes the following arguments:
.sp
.ne 2
.mk
.na
\fB\fIparcor\fR\fR
.ad
.RS 10n
.rt  
The partial correlation (PARCOR) coefficients.
.RE

.sp
.ne 2
.mk
.na
\fB\fIpscale\fR\fR
.ad
.RS 10n
.rt  
The scaling factor of the partial correlation (PARCOR) coefficients, where \fBactual_data = output_data * 2**(-scaling_factor)\fR.
.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
Each 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_SignalLPCAutoCorrelInit_S16\fR(3MLIB), \fBmlib_SignalLPCAutoCorrel_S16\fR(3MLIB), \fBmlib_SignalLPCAutoCorrelGetEnergy_S16\fR(3MLIB), \fBmlib_SignalLPCAutoCorrelFree_S16\fR(3MLIB), \fBattributes\fR(5)