function Px = min_norm(x,p,M)
%MIN_NORM Frequency estimation using the minimum norm algorithm.
%--------
%USAGE	Px = min_norm(x,p,M)
%
%	The input sequence x is assumed to consist of p complex
%	exponentials in white noise.  The frequencies of the
%	complex exponentials and the variance of the white noise
%	are estimated using the minimum norm algorithm.  
%
%	x : input sequence
%	p : Number of complex exponential in x
%	M : Size of the autocorrelation matrix to use in
%	      estimating the complex exponential frequencies
%
%	The frequency estimates are found from the peaks of the
%	pseudospectrum Px.
%
%  see also PHD, EV, and MUSIC
%
%---------------------------------------------------------------
% copyright 1996, by M.H. Hayes.  For use with the book 
% "Statistical Digital Signal Processing and Modeling"
% (John Wiley & Sons, 1996).
%---------------------------------------------------------------
%

   x   = x(:);
   if N<p+1, error('Specified size of R is too small'), end
   R=covar(x,N);
   [v,d]=eig(R);
   [y,i]=sort(diag(d));
   for j=1:N-p
       V=[V,v(:,i(j))];
       end;
   a=V*V(1,:)';
   Px=-20*log10(abs(fft(a,1024)));
   end;