## SPcovPmse

#### Routine

double SPcovPmse (const float pc[], const float *Cov[], int Np)

#### Purpose

Calculate the mean-square prediction error (covariance specified)

#### Description

This function calculates the squared prediction error for a linear predictor. Consider a linear predictor with Np coefficients,

              Np
      y(k) = SUM p(i) x(k-i) ,
             i=1

where x(i) is the input signal. The prediction error is

      e(k) = x(k) - y(k) .

The mean-square prediction error is E[e(k)^2] or in vector-matrix notation

      E = Ex - 2 p'r + p'R p .

The mean-square value Ex, matrix R and vector p are defined as follows

          Ex = Cov(0,0) = E[x(k)^2]
      R(i,j) = Cov(i,j) = E[x(k-i) x(k-j)],  for 1 <= i,j <= Np,
        r(i) = Cov(0,i) = E[x(k) x(k-i)],    for 1 <= i <= Np.

The expectation operator E[.] is often replaced by a sum over k over a finite interval.

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

#### Parameters

<- double SPcovPmse
  Resulting filter error energy
-> const float pc[]
  Np element vector of predictor coefficients. Coefficient pc[i] is the predictor coefficient corresponding to lag i+1.
-> const float *Cov[]
  Cov is an array of pointers to the rows of an Np+1 by Np+1 symmetric positive definite correlation matrix. Only the lower triangular portion of Cov is accessed. Note that with ANSI C, if the actual parameter is not declared to have the const attribute, an explicit cast to (const float **) is required.
-> int Np
  Number of predictor coefficients

#### Author / revision

P. Kabal / Revision 1.7 2003/05/09

#### See Also

SPcovCXpc, SPcovLXpc, SPcovMXpc, SPcovXpc

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