phd.m

solution for the Statistical modelling for digital signal processing by hayes

function [a,sigma] = phd(x,p)

%PHD	Frequency estimation using the Pisarenko harmonic decomposition.

%---

%USAGE	[a,sigma] = phd(x,p)

%

%	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 Pisarenko harmonic decomposition.  

%

%	The frequency estimates are found from the peaks of the

%	pseudospectrum

%			         1

%		-----------------------------------

%		1 + a(1)exp(jw) + ... + a(p)exp(jpw)	

%

%	or from the roots of the polynomial formed from the 

%	vector a.  The estimate of the white noise variance is 

%	returned in sigma.

%

%  see also MUSIC, EV, and MIN_NORM

%

%---------------------------------------------------------------

% copyright 1996, by M.H. Hayes.  For use with the book 

% "Statistical Digital Signal Processing and Modeling"

% (John Wiley & Sons, 1996).

%---------------------------------------------------------------



   x = x(:);

   R = covar(x,p+1);

   [v,d]=eig(R);

   sigma=min(diag(d));

   index=find(diag(d)==sigma);

   a = v(:,index);

   end;