TSP (libtsp) - SPrcXpc

SPrcXpc

Routine

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

Purpose

Convert reflection coefficients to predictor coefficients

Description

This routine generates the vector of predictor coefficients corresponding to the given set of reflection coefficients. The relationship between the reflection coefficients, k(i), and the predictor coefficients p(i) is determined from the following update equations. The predictor coefficients at iteration j+1 (primed quantities) are determined from reflection coefficient j and the predictor coefficients at iteration j.

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

This algorithm requires

  Np*(Np-1)/2 multiplies and
  Np*(Np-1)/2 adds.

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.

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

Parameters

<- double SPrcXpc: Normalized mean-square prediction error. This is the energy of the prediction residual for a case in which the given reflection coefficients are matched to the signal. Note that this value may be negative if the given reflection coefficients exceed unity in magnitude.
-> const float rc[]: Vector of Np reflection coefficients. The sign of these coefficients is assumed to be such that rc[Np-1] = -pc[Np-1].
<- 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.
-> int Np: Number of coefficients

Author / revision