SPcorPmse
Routine
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double SPcorPmse (const float pc[], const float rxx[], int Np)
Purpose
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Calculate the mean-square prediction error
Description
This function calculates the mean-square 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(k) 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 = 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.
For this routine, the matrix R must be symmetric and Toeplitz. Then
R(i,j) = rxx(|i-j|)
r(i) = rxx(i)
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
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<- double SPcorPmse
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Resultant mean-square prediction error
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-> const float pc[]
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Np element vector of predictor coefficients. Coefficient pc[i] is the
predictor coefficient corresponding to lag i+1.
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-> const float rxx[]
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Np+1 element vector of autocorrelation values. Element rxx[i] is the
autocorrelation at lag i.
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-> int Np
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Number of predictor coefficients
Author / revision
P. Kabal Copyright (C) 1996
/ Revision 1.4 1996/05/31
See Also
SPcorXpc
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