## SPcovFmse

#### Routine

double SPcovFmse (const float h[], double Ed, const float *R[], const float r[], int N)

#### Purpose

Find the mean-square error for a filter (covariance specified)

#### Description

This function calculates the mean-square error for a linear estimation problem. Consider a filter with N coefficients, with coefficient h(i) corresponding to lag D(i). The filter output is
```         N-1
y(k) = SUM h(i) x(k-D(i)) ,
i=0
```
where x(i) is the input signal. The filter error is

```  e(k) = d(k) - y(k) ,
```

where d(k) is the desired signal. The mean-square filtering error can be expressed as

```  ferr = Ed - 2 h'r + h'R h .
```

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

```      Ed = E[d(k)^2]
R(i,j) = E[x(k-D(i)) x(k-D(j))],  for 0 <= i,j < N,
r(i) = E[d(k) x(k-D(i))],       for 0 <= i < N.
```

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

#### Parameters

<- double SPcovFmse
Resultant filter error energy
-> const float h[]
N element vector of filter coefficients. Coefficient h[i] is the filter coefficient corresponding to lag N1+i.
-> double Ed
Signal energy for the desired signal
-> const float *R[]
R is an array of pointers to the rows of an N by N positive definite correlation matrix. Only the lower triangular portion of R 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. -> const float r[] N element vector of cross-correlation values
-> int N
Number of filter coefficients

#### Author / revision

P. Kabal / Revision 1.5 2003/05/09