## SPlsfXpc

#### Routine

void SPlsfXpc (const float lsf[], float pc[], int Np)

#### Purpose

Convert LSF's to predictor coefficients

#### Description

This routine converts a vector of line spectral frequencies to the corresponding vector of predictor coefficients. The LSF's are the frequencies (angles) corresponding to roots on the unit circle. These roots are the roots of two polynomials, one symmetric, the other anti-symmetric. The odd-numbered LSF's specify roots of one polynomial, while the even- numbered LSF's specify the roots of the other polynomial. The polynomials are formed by the polynomial multiplication of the factors representing conjugate pairs of roots. The predictor coefficients are formed by the addition of the two polynomials.

Line spectral frequencies and predictor coefficients are usually expressed algebraically as vectors with one-offset indexing. The correspondence to the zero-offset C-arrays is as follows.

```  l(1) <==> lsf       first (lowest frequency) line spectral frequency
l(i) <==> lsf[i-1]     1 <= i < Np
p(1) <==> pc        predictor coefficient corresponding to lag 1
p(i) <==> pc[i-1]      1 <= i < Np
```

#### Parameters

-> const float lsf[]
Array of Np line spectral frequencies. Each line spectral frequency lies in the range 0 to pi. If the LSF's are well-ordered (ascending order), the resulting predictor corresponds to a minimum phase prediction error filter.
-> int Np
Number of coefficients (at most 50)
<- float pc[]
Output array of Np predictor coefficients. These are the coefficients of the predictor filter, with pc being the predictor coefficient corresponding to lag 1, and pc[Np-1] corresponding to lag Np.
-> int Np
Number of coefficients (at most 50)

#### Author / revision

P. Kabal / Revision 1.21 2003/05/09