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function [ar, sigma2,rc] = levin(r);
// //[ar,sigma2,rc]=lev(r)
// //Resolve the Yule-Walker equations:
// //
// // |r(0) r(1) ... r(N-1)|| a(1) | |sigma2|
// // |r(1) r(0) ... r(n-1)|| a(2) | | 0 |
// // | : : ... : || : |=| 0 |
// // | : : ... : || : | | 0 |
// // |r(N-1) r(N-2) ... r(0) ||a(N-1)| | 0 |
// //
// //using Levinson's algorithm.
// // r :Correlation coefficients
// // ar :Auto-Regressive model parameters
// // sigma2 :Scale constant
// // rc :Reflection coefficients
// Example :
if length(r)==1 then
ar=1;
sigma2=r;
rc=[];
else
ar = 0;
aj(1) = 1;
ej = r(1);
rc = [];
p=length(r)-1
for j=1:p,
aj1 = zeros(j+1, 1);
aj1(1) = 1;
gammaj = r(j+1);
for i=2:j,
gammaj = gammaj + aj(i)*r(j-i+2);
end
if ej==0 then
lambdaj1=%nan
else
lambdaj1 = -gammaj/ej;
end
rc=[rc; lambdaj1];
for i=2:j,
aj1(i) = aj(i)+lambdaj1*(aj(j-i+2)');
end
aj1(j+1) = lambdaj1;
ej1 = ej*(1-abs(lambdaj1)^2);
aj = aj1;
ar = aj1;
ej = ej1;
end
sigma2 = sqrt(ej1);
end
endfunction
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