Toeplitz system solver by Levinson algorithm (multidimensional) (original) (raw)

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levin

Toeplitz system solver by Levinson algorithm (multidimensional)

Calling Sequence

Arguments

A scalar with integer value: the maximum order of the filter

cov

A (nlag*d) x d matrix. It contains theRk (d x d matrices for ad-dimensional process) stored in the following way :

A list, the successively calculated Levinson polynomials (degree 1 to n), with coefficientsAk

sig

A list, the successive mean-square errors.

Description

function which solves recursively on n the following Toeplitz system (normal equations)

where {Rk;k=1:nlag} is the sequence ofnlag empirical covariances

Examples

t1=0:.1:100;rand('normal'); y1=sin(2*%pit1)+sin(2%pi2t1);y1=y1+rand(y1);plot(t1,y1);

nlag=128; c1=corr(y1,nlag); c1=c1';

n=15; [la1,sig1]=levin(n,c1);

for i=1:n, s1=roots(la1(i));s1=log(s1)/2/%pi/.1;

s1=gsort(imag(s1));s1=s1(1:i/2);end;

d=2;dt=0.1; nlag=64; t2=0:2*%pidt:100; y2=[sin(t2)+sin(2t2)+rand(t2);sin(3t2)+sin(4t2)+rand(t2)]; c2=[]; for j=1:2, for k=1:2, c2=[c2;corr(y2(k,:),y2(j,:),nlag)];end;end; c2=matrix(c2,2,128);cov=[]; for j=1:64,cov=[cov;c2(:,(j-1)d+1:jd)];end; c2=cov;