SPcovLXpc
Routine

double SPcovLXpc (const float *Cov[], float pc[], int Np)
Purpose

Find predictor coefficients using the covariance lattice method
Description
This routine calculates the parameters for a lattice predictor which
minimizes the sum of the forward and backward errors. The reflection
coefficients which describe the lattice filter are converted to the predictor
coefficients which are returned. This procedure guarantees a minimum phase
prediction error filter.
Consider a linear predictor with Np coefficients,
Np
y(k) = SUM p(i) x(ki) ,
i=1
where x(i) is the input signal. This routine finds the predictor
cofficients.
This procedure is based on Makhoul's covariance lattice method. The
reflection coefficients are chosen to minimize the sum of the forward and
backward prediction errors.
The computation uses a correlation matrix Cov with elements defined as
Cov(i,j) = E[x(ki) x(kj)], for 0 <= i,j <= Np.
The expectation operator E[.] is often replaced by a sum over k over a finite
interval. Minimization of the prediction error over this interval defines
the socalled covariance method for determining the linear prediction
coefficients.

Reference:

1: J. Makhoul, "Stable and efficient lattice methods for linear prediction",
IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP25, pp.
423428, October 1977.
Predictor coefficients are usually expressed algebraically as vectors with
1offset indexing. The correspondence to the 0offset Carrays is as
follows.
p(1) <==> pc[0] predictor coefficient corresponding to lag 1
p(i) <==> pc[i1] 1 <= i < Np
Parameters

< double SPcovCXpc

Resultant prediction error energy

> const float *Cov[]

Cov is an array of pointers to the rows of an Np+1 by Np+1 symmetric
positive definite correlation matrix. Only the lower triangular portion
of Cov 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 pc[]

Np element vector of predictor coefficients. Coefficient pc[i] is the
predictor coefficient corresponding to lag i+1.

> int Np

Number of prediction coefficients
Author / revision
P. Kabal
/ Revision 1.9 2003/05/09
See Also
SPcovCXpc,
SPcovar
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