function Px = bt_pc(x,p,M)
%BT_PC	Frequency estimation using principal components Blackman-Tukey.
%-----
%USAGE	Px = bt_pc(x,p,M)
%
%	The spectrum of a process x is estimated using a principal
%	components analysis of the autocorrelation matrix.
%	The model for the process is that x(n) consists of a sum of 
%	complex exponentials in white noise.  
%	After a principle components analysis, the principal eigenvectors
%	are used in the Blackman-Tukey estimate.
%
%          x  : input sequence
%          p  : number of complex exponentials in x
%          M  : size of autocorrelation matrix
%
%	The spectrum estimate is returned in Px using a dB scale.
%
%---------------------------------------------------------------
% copyright 1996, by M.H. Hayes.  For use with the book 
% "Statistical Digital Signal Processing and Modeling"
% (John Wiley & Sons, 1996).
%---------------------------------------------------------------

   x   = x(:);
   if M<p+1, error('Specified size of R is too small'), end
   R=covar(x,M);
   [v,d]=eig(R);
   [y,i]=sort(diag(d));
   Px=0;
   for j=M-p+1,M;
       Px=Px+abs(fft(v(:,i(j)),1024))*sqrt(real(y(j)));
       end;
   Px=20*log10(Px)-10*log10(M);
   end;