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<HTML>
<HEAD>
<TITLE>TSP (libtsp/SP) - SPrcXpc</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFACD">
<H2>SPrcXpc</H2>
<HR>
<H4>Routine</H4>
<DL>
<DT>
double SPrcXpc (const float rc[], float pc[], int Np)
</DL>
<H4>Purpose</H4>
<DL>
<DT>
Convert reflection coefficients to predictor coefficients
</DL>
<H4>Description</H4>
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>
<PRE>
p'(j) = -k(j)
p'(i) = p(i) + k(j) p(j-i) , 1 < i < j
</PRE>
<P>
This algorithm requires
<PRE>
Np*(Np-1)/2 multiplies and
Np*(Np-1)/2 adds.
</PRE>
<P>
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.
<PRE>
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
</PRE>
<H4>Parameters</H4>
<DL>
<DT>
<- double SPrcXpc
<DD>
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.
<DT>
-> const float rc[]
<DD>
Vector of Np reflection coefficients. The sign of these coefficients is
assumed to be such that rc[Np-1] = -pc[Np-1].
<DT>
<- float pc[]
<DD>
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.
<DT>
-> int Np
<DD>
Number of coefficients
</DL>
<H4>Author / revision</H4>
P. Kabal Copyright (C) 1997
/ Revision 1.13 1997/10/10
<H4>See Also</H4>
<A HREF="SPcepXpc.html">SPcepXpc</A>,
<A HREF="SPcorXpc.html">SPcorXpc</A>,
<A HREF="SPecXpc.html">SPecXpc</A>,
<A HREF="SPlsfXpc.html">SPlsfXpc</A>
<P>
<HR>
Main Index <A HREF="../libtsp.html">libtsp</A>
</BODY>
</HTML>
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