schurrc - Compute reflection coefficients from autocorrelation sequence

Syntax

Description

k = schurrc(r) uses the Schur algorithm to compute a vector k of reflection coefficients from a vector r representing an autocorrelation sequence. k and r are the same size. The reflection coefficients represent the lattice parameters of a prediction filter for a signal with the given autocorrelation sequence, r. When r is a matrix, schurrc treats each column of r as an independent autocorrelation sequence, and produces a matrix k, the same size as r. Each column of k represents the reflection coefficients for the lattice filter for predicting the process with the corresponding autocorrelation sequence r.

[k,e] = schurrc(r) also computes the scalar e, the prediction error variance. When r is a matrix, e is a column vector. The number of rows of e is the same as the number of columns of r.

Examples

Create an autocorrelation sequence from the MATLAB speech signal contained in mtlb.mat, and use the Schur algorithm to compute the reflection coefficients of a lattice prediction filter for this autocorrelation sequence:

load mtlb
r = xcorr(mtlb(1:5),'unbiased');
k = schurrc(r(5:end))
k =
   -0.7583
    0.1384
    0.7042
   -0.3699

References

[1] Proakis, J. and D. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, Third edition, Prentice-Hall, 1996, pp.868-873.

See Also

levinson

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