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<HTML>
<HEAD>
<TITLE>TSP (libtsp/SP) - SPcorPmse</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFACD">
<H2>SPcorPmse</H2>
<HR>
<H4>Routine</H4>
<DL>
<DT>
double SPcorPmse (const float pc[], const float rxx[], int Np)
</DL>
<H4>Purpose</H4>
<DL>
<DT>
Calculate the mean-square prediction error
</DL>
<H4>Description</H4>
This function calculates the mean-square prediction error for a linear
predictor. Consider a linear predictor with Np coefficients,
<PRE>
Np
y(k) = SUM p(i) x(k-i) ,
i=1
</PRE>
where x(k) is the input signal. The prediction error is
<P>
<PRE>
e(k) = x(k) - y(k) .
</PRE>
<P>
The mean-square prediction error is E[e(k)^2] or in vector-matrix notation
<P>
<PRE>
E = Ex - 2 p'r + p'R p ,
</PRE>
<P>
The mean-square value Ex, matrix R and vector p are defined as follows
<PRE>
Ex = E[x(k)^2]
R(i,j) = E[x(k-i) x(k-j)], for 1 <= i,j <= Np,
r(i) = E[x(k) x(k-i)], for 1 <= i <= Np.
</PRE>
<P>
For this routine, the matrix R must be symmetric and Toeplitz. Then
<P>
<PRE>
R(i,j) = rxx(|i-j|)
r(i) = rxx(i)
</PRE>
<P>
Predictor coefficients are usually expressed algebraically as vectors with
1-offset indexing. The correspondence to the 0-offset C-arrays is as
follows.
<PRE>
p(1) <==> pc[0] predictor coefficient corresponding to lag 1
p(i) <==> pc[i-1] 1 <= i < Np
</PRE>
<H4>Parameters</H4>
<DL>
<DT>
<- double SPcorPmse
<DD>
Resultant mean-square prediction error
<DT>
-> const float pc[]
<DD>
Np element vector of predictor coefficients. Coefficient pc[i] is the
predictor coefficient corresponding to lag i+1.
<DT>
-> const float rxx[]
<DD>
Np+1 element vector of autocorrelation values. Element rxx[i] is the
autocorrelation at lag i.
<DT>
-> int Np
<DD>
Number of predictor coefficients
</DL>
<H4>Author / revision</H4>
P. Kabal Copyright (C) 1996
/ Revision 1.4 1996/05/31
<H4>See Also</H4>
<A HREF="SPcorXpc.html">SPcorXpc</A>
<P>
<HR>
Main Index <A HREF="../libtsp.html">libtsp</A>
</BODY>
</HTML>
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