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//schurrc - Schur algorithm.
//K = SCHURRC(R) computes the reflection coefficients from autocorrelation vector R. If R is a matrix, SCHURRC finds coefficients for each column of R, and returns them in the columns of K.
//[K,E] = SCHURRC(R) returns the prediction error variance E. If R is a matrix, SCHURRC finds the error for each column of R, and returns them in the rows of E.
//Modified to match matlab i/p and o/p and handle exceptions
//Fixed bugs
//by Debdeep Dey
//////EXAMPLES:
//m=linspace(1,100);
//r = xcorr(m(1:5),'unbiased');.......autocorrelation vector
//[k,e] = schurrc(r(5:$))
//EXPECTED OUTPUT
//e =1.6212406
//k = - 0.9090909 0.2222222 0.2244898 0.2434211
function [k,e] = schurrc(R)
narginchk(1,1,argn(2));
if(type(R)==10) then// R is a matrix of character strings
w=R;
[nr,nc]=size(R);
if(nr==1 & nc==1) then
R=ascii(R);//conversion to the corresponding asci values
R=matrix(R,length(w));//reshaping the matrix
else
R=ascii(R);
R=matrix(R,size(w));//reshaping the matrix
end
end
if(type(R) > 1) then ///checking if R in not a matrix of real or complex numbers
error('Input R is not a matrix')
end
if (min(size(R)) == 1) then
R = R(:);
end
[m,n] = size(R);
// Compute reflection coefficients for each column of the input matrix
for j = 1:n
X = R(:,j).';
// Schur's iterative algorithm on a row vector of autocorrelation values
U = [0 X(2:m); X(1:m)];
for i = 2:m,
U(2,:) = [0 U(2,1:m-1)];
k(i-1,j) = -U(1,i)/U(2,i);
U = [1 k(i-1,j); conj(k(i-1,j)) 1]*U;
end
e(j,1) = U(2,$);
end
endfunction
function narginchk(l,h,t)
if t<l then
error("Too few input arguments");
elseif t>l then
error("Too many input arguments");
end
endfunction
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