man pages section 3: Multimedia Library Functions
Updated: July 2014

## mlib_SignalLPCAutoCorrelGetPARCOR_F32(3MLIB)

### Name

mlib_SignalLPCAutoCorrelGetPARCOR_F32 - return the partial correlation (PARCOR) coefficients

### Synopsis

```cc [ flag... ] file... –lmlib [ library... ]
#include <mlib.h>

mlib_status mlib_SignalLPCAutoCorrelGetPARCOR_F32(
mlib_f32 *parcor, void *state);```

### Description

The mlib_SignalLPCAutoCorrelGetPARCOR_F32() function returns the partial correlation (PARCOR) coefficients.

In linear predictive coding (LPC) model, each speech sample is represented as a linear combination of the past M samples.

```	        M
s(n) = SUM a(i) * s(n-i) + G * u(n)
i=1```

where s(*) is the speech signal, u(*) is the excitation signal, and G is the gain constants, M is the order of the linear prediction filter. Given s(*), the goal is to find a set of coefficient a(*) that minimizes the prediction error e(*).

```	               M
e(n) = s(n) - SUM a(i) * s(n-i)
i=1```

In autocorrelation method, the coefficients can be obtained by solving following set of linear equations.

```	 M
SUM a(i) * r(|i-k|) = r(k), k=1,...,M
i=1```

where

```	      N-k-1
r(k) = SUM s(j) * s(j+k)
j=0```

are the autocorrelation coefficients of s(*), N is the length of the input speech vector. r(0) is the energy of the speech signal.

Note that the autocorrelation matrix R is a Toeplitz matrix (symmetric with all diagonal elements equal), and the equations can be solved efficiently with Levinson-Durbin algorithm.

See Fundamentals of Speech Recognition by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.

### Parameters

The function takes the following arguments:

parcor

The partial correlation (PARCOR) coefficients.

state

Pointer to the internal state structure.

### Return Values

The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE.

### Attributes

See attributes(5) for descriptions of the following attributes:

ATTRIBUTE TYPE
ATTRIBUTE VALUE
Interface Stability
Committed
MT-Level
MT-Safe