Given the transfer function [H(z)=frac{zleft[z-cos left(omega_{0} ight) ight]}{z^{2}-2 cos left(omega_{0} ight) z+1}] (a) Where are its poles

Given the transfer function

\[H(z)=\frac{z\left[z-\cos \left(\omega_{0}\right)\right]}{z^{2}-2 \cos \left(\omega_{0}\right) z+1}\]

(a) Where are its poles located exactly on the unit circle?

(b) Using \(2 \cos \left(\omega_{0}\right)=-2,0,1,2\), and without any external excitation, place an initial value of 0.5 in one of the filter states and determine the output signal for a few hundred iterations. Comment on the observed results.