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<HTML>
<HEAD>
<TITLE>TSP (libtsp/SP) - SPcorFmse</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFACD">
<H2>SPcorFmse</H2>
<HR>
<H4>Routine</H4>
<DL>
<DT>
double SPcorFmse (const float h[], double Ed, const float rxx[],
const float r[], int N)
</DL>
<H4>Purpose</H4>
<DL>
<DT>
Calculate the mean-square filtering error
</DL>
<H4>Description</H4>
This function calculates the mean-square error for a linear filter. Consider
a filter with N coefficients, with coefficient h(i) corresponding to
lag Nd+i. The filter output is
<PRE>
N-1
y(k) = SUM h(i) x(k-i-Nd) ,
i=0
</PRE>
where x(i) is the input signal. The filter error is
<P>
<PRE>
e(k) = d(k) - y(k) ,
</PRE>
<P>
where d(k) is the desired signal. The mean-square filtering error is
E[e(k)^2] or in vector-matrix notation
<P>
<PRE>
ferr = Ed - 2 h'r + h' R h ,
</PRE>
<P>
The mean-square value E0, matrix R and vector p are defined as follows
<P>
<PRE>
Ed = E[d(k)^2]
R(i,j) = E[x(k-i-Nd) x(k-j-Nd], for 0 <= i,j < N,
r(i) = E[d(k) x(k-i-Nd)], for 0 <= i < N.
</PRE>
<P>
For this routine, the matrix R must be symmetric and Toeplitz, viz.
<P>
<PRE>
R(i,j) = rxx(|i-j|).
</PRE>
<P>
Linear prediction can be cast into the above form, if we let Nd=1. Also
for linear prediction, usually d(k)=x(k), giving r(i)=rxx(i).
<H4>Parameters</H4>
<DL>
<DT>
<- double SPcorFmse
<DD>
Resultant mean-square error
<DT>
-> const float h[]
<DD>
N element vector of filter coefficients. Coefficient h[i] is the filter
coefficient corresponding to lag Nd+i.
<DT>
-> double Ed
<DD>
Signal energy for the desired signal. This value is used only for the
computation of the mean-square error.
<DT>
-> const float rxx[]
<DD>
N element vector of autocorrelation values. Element rxx[i] is the
autocorrelation at lag i.
<DT>
-> const float r[]
<DD>
N element vector of cross-correlation values. Element r[i] is the
cross-correlation at lag Nd+i.
<DT>
-> int N
<DD>
Number of elements in each of the vectors rxx, h and r.
</DL>
<H4>Author / revision</H4>
P. Kabal Copyright (C) 1996
/ Revision 1.10 1996/04/17
<H4>See Also</H4>
<A HREF="SPcorFilt.html">SPcorFilt</A>
<P>
<HR>
Main Index <A HREF="../libtsp.html">libtsp</A>
</BODY>
</HTML>
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