Question

alpha = 5.0

beta = 7.1

zeta = 6.9

PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.

Answer 1

1)matlab code

clear;clc;
%% transfer function and it's poles and zeros
%given data
a=5;%alpha value
b=7.1;%beta value
z=6.9;%zeta value
num=[a,2*b,z];%numerator coefficient
den=[1,-a/10,(a^2)/100];%denominator coefficient
Hz=tf(num,den,-1);
zr=zero(Hz);%zeros of H(Z)
po=pole(Hz);%poles of H(z)
disp(['zeros of H(z) z=',num2str(zr(1)),',',num2str(zr(2))]);
disp(['poles of H(z) z=',num2str(po(1)),',',num2str(po(2))]);
%% pole zero plot on zplane
figure(1)
zplane(num,den);
title('pole-zero plot of H(z)=(\alpha+2\betaZ^{-1}+\zetaZ^{-2})/(1-(\alpha/10)Z^{-1}+(\alpha^2)Z^{-2})');
%% magnitude plot and phase plot of H(z)
figure(2)
freqz(num,den);
title('frequency responce plot of H(z)=(\alpha+2\betaZ^{-1}+\zetaZ^{-2})/(1-(\alpha/10)Z^{-1}+(\alpha^2)Z^{-2})');

2)matlab plot and result

zeros of H(z) z=-2.2177,-0.62225
poles of H(z) z=0.25+0.43301i,0.25-0.43301i