# PIsarenko Harmonic Decomposition method for PSD estimation

i would like to present steps for estimation Power Spectrum density using Pisarneko Harmonic Decomposition

i would like to present code for step 1 part

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

% the Pisarenko Harmonic decomposition
x=x(:);
R=Covar(x,p+1);
[v,d]=eig(R);
sigma=min(diag(d));
index=find(diag(d)==sigma);
vmin=v(:,index);
end

now let us consider following time series

fs=100;
ts=1/fs;
t=0:ts:2.93;
x=10*sin(2*pi*10*t)+15*cos(2*pi*10.5*t)+14*sin(2*pi*10.19*t)+3*randn(size(t));

PSD using music method can be estimated as follow

pmusic(x,6);

how can i got the same result using pisrenko harmonic decomposition? thanks in advance

Since you have $v_{min}$, the eigenvector corresponding to the minimum eigenvalue, compute the function $\hat{P}_{PHD}(e^{j\omega})$.
The vector $e$ is given by $e = [1 \quad e^{j\omega} \quad e^{2j\omega} \ldots e^{pj\omega}]$
Make a plot of $\hat{P}_{PHD}(e^{j\omega})$ and measure the $p=3$ peaks to find the frequencies.
• You don't need to compute the Z transform, the equation for $\hat{P}_{PHD}$is all you need – Robert L. Feb 26 '17 at 20:58