function [a,b,err] = prony(x,p,q)
%PRONY	Model a signal using Prony's method
%----
%Usage: [a,b,err] = prony(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, SHANKS
%
%---------------------------------------------------------------
% 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
X   = convm(x,p+1);
Xq  = X(q+1:N+p-1,1:p);
a   = [1;-Xq\X(q+2:N+p,1)];
b   = X(1:q+1,1:p+1)*a;
err = x(q+2:N)'*X(q+2:N,1:p+1)*a;
end;