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//This function fits an AR (p)-model with Yule-Walker estimates.
//Calling Sequence
//a = aryule (x, p)
//[a, v] = aryule (x, p)
//[a, v, k] = aryule (x, p)
//Parameters
//x: vector of real or complex numbers, length > 2
//p: positive integer value < length(x) - 1
//a: gives the AR coefficients
//v: gives the variance of the white noise,
//k: gives the reflection coefficients to be used in the lattice filter
//Description
//This function fits an AR (p)-model with Yule-Walker estimates.
//The first argument is the data vector which is to be estimated.
//Examples
//aryule([1,2,3,4,5],2)
//ans =
// 1. - 0.8140351 0.1192982
//*************************************************************************************
//-------------------version1 (using callOctave / errored)-----------------------------
//*************************************************************************************
//function [a, v, k] = aryule (x, p)
//funcprot(0);
//rhs = argn(2)
//lhs = argn(1)
//
//if(rhs~=2)
//error("Wrong number of input arguments.")
//end
//
// select(lhs)
// case 1 then
// a = callOctave("aryule",x,p)
// case 2 then
// [a,v] = callOctave("aryule",x,p)
// case 3 then
// [a,v,k] = callOctave("aryule",x,p)
// end
//
//endfunction
//*************************************************************************************
//-----------------------------version2 (pure scilab code)-----------------------------
//*************************************************************************************
function [a, v, k] = aryule (x, p)
[nargout,nargin] = argn() ;
if ( nargin~=2 )
error('aryule : invalid number of inputs');
elseif ( ~isvector(x) | length(x)<3 )
error( 'aryule: arg 1 (x) must be vector of length >2' );
elseif ( ~isscalar(p) | fix(p)~=p | p > length(x)-2 )
error( 'aryule: arg 2 (p) must be an integer >0 and <length(x)-1' );
end
c = xcorr(x, p+1, 'biased');
c(1:p+1) = []; // remove negative autocorrelation lags
c(1) = real(c(1)); // levinson/toeplitz requires exactly c(1)==conj(c(1))
if nargout <= 1
a = levinson(c, p);
elseif nargout == 2
[a, v] = levinson(c, p);
else
[a, v, k] = levinson(c, p);
end
endfunction
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