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

## mlib_SignalLSP2LPC_F32(3MLIB)

### Name

mlib_SignalLSP2LPC_F32 - convert line spectral pair coefficients to linear prediction coefficients

### Synopsis

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

mlib_status mlib_SignalLSP2LPC_F32(mlib_f32 *lpc,
const mlib_f32 *lsp, mlib_s32 order);```

### Description

The mlib_SignalLSP2LPC_F32() function converts line spectral pair coefficients to linear prediction coefficients.

The line spectral pair (LPS) coefficients are defined as the roots of the following two polynomials:

```	               -(M+1)     -1
P(z) = A(z) + z      * A(z  )

-(M+1)     -1
Q(z) = A(z) - z      * A(z  )```

where A(z) is the inverse filter

```	           M          -i
A(z) = 1- SUM a(i) * z
i=1```

Note that since P(z) is symmetric and Q(z) is antisymmetric all roots of these polynomials are on the unit circle and they alternate each other. P(z) has a root at z = -1 (w = PI) and Q(z) has a root at z = 1 (w = 0).

The line spectral frequency (LPF) are the angular frequency of the line spectral pair (LPS) coefficients.

`	q = cos(w)`

where q is the LPS and w is the LPF.

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

### Parameters

The function takes the following arguments:

lpc

The linear prediction coefficients.

lsp

The line spectral pair coefficients.

order

The order of the linear prediction filter.

### 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