## SPpcXrc

#### Routine

double SPpcXrc (const float pc[], float rc[], int Np)

#### Purpose

Convert predictor coefficients to reflection coefficients

#### Description

The given predictor coefficients are converted to reflection coefficients using a recursive algorithm. The reflection coefficients lie between -1 and +1 if the corresponding synthesis filter is stable. The procedure implements the following step-down recursion to get the reflection coefficients k(j) from the initial set of predictor coefficients. The iteration index runs from Np to 1. For each order j, the step-down procedure finds the predictor coefficients for a predictor of order j-1 from the predictor coefficients for a predictor of order j. The equations are as follows, where the primed primed quantities indicate the j-1 term predictor obtained at iteration j.

      k(j) = -p(j)

              p(i) - k(j) p(j-i)
      p'(i) = ------------------ ,   0 < i < j,
                1 - k(j) k(j)

Reflection coefficients and predictor coefficients are usually expressed algebraically as vectors with 1-offset indexing. The correspondence to the 0-offset C-arrays is as follows.

      p(1) <==> pc[0]       predictor coefficient corresponding to lag 1
      p(i) <==> pc[i-1]     1 <= i < Np
      k(1) <==> rc[0]       first reflection coefficient
      k(i) <==> rc[i-1]     1 <= i < Np

#### Parameters

<- double SPpcXrc
  Normalized mean-square prediction error. This is the energy of the prediction residual for a case in which the given predictor coefficients are matched to the signal. Note that this value may be negative if the given predictor coefficients do not correspond to a minimum phase prediction error filter.
-> const float pc[]
  Vector of predictor coefficients (Np values). These are the coefficients of the predictor filter, with pc[0] being the predictor coefficient corresponding to lag 1, and pc[Np-1] corresponding to lag Np.
<- float rc[]
  Vector of Np reflection coefficients. The sign of these coefficients is such that rc[Np-1] = -pc[Np-1].
-> int Np
  Number of coefficients

#### Author / revision

P. Kabal / Revision 1.15 2003/05/09

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