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;