function [a,b,err] = shanks(x,p,q)
%SHANKS	Model a signal using Shanks' method 
%----
%Usage: [a,b,err] = shanks(x,p,q) 
%
%	The sequence x is modeled as the unit sample response of
%	a filter having a system function of the form
%		H(z) = B(z)/A(z) 
%	The polynomials B(z) and A(z) are formed from the vectors
%		b=[b(0), b(1), ... b(q)]
%		a=[1   , a(1), ... a(p)]
%	The input q defines the number of zeros in the model
%	and p defines the number of poles.  The modeling error
%	is returned in err.
%
%  see also ACM, COVM, PADE, PRONY
%
%---------------------------------------------------------------
% copyright 1996, by M.H. Hayes.  For use with the book 
% "Statistical Digital Signal Processing and Modeling"
% (John Wiley & Sons, 1996).
%---------------------------------------------------------------

x   = x(:);
N   = length(x);
if p+q>=length(x), error('Model order too large'), end
a   = prony(x,p,q);
u   = [1; zeros(N-1,1)];
g   = filter(1,a,u);
G   = convm(g,q+1);
b   = G(1:N,:)\x;
err = x'*x-x'*G(1:N,1:q+1)*b;
end;

