Question

MATLAB The z-transform of LTI systems can be expressed as a ratio of two polynomials in z-1 Also, the rational z-transform can be written in factored form N-M) for z → H(G) = 0, the values of z are the zeros of the system for z = p2 → H(p) = oo, the values of z are the poles of the system Use MATLAB to graph Y() 1-242+2882 x(2) 1-0.8 -2 H(z) = 0,82-1 +0 642 Hints: e z: is a complex number euse: o x-linspacel-4,4,256); o y linspacef-4,4,256); use "meshgrid" function in MATLAB to create re z (real part) and im z (imaginary part) to be used as real and imaginary part of z. Also make sure you use scalar multiplication power and division (". and ".") use "mesh" to graph, for H(z), use logarithmic scale for H(z) Use MATLAB .Determine poles and zeros. Hint: "tf2zpk" function Graph poles and zeros. Hint: "zplane" function e Plot the frequency response. Hint: "regz" function

Answer 1

MATLAB CODE:

clc
clear all
close all

syms z

H(z) = (1-2.4*z^-1+2.88*z^-2)/(1-0.8*z^-1+0.64*z^-2);

Numerator = [1 -2.4 2.88];
Denominator = [1 -0.8 0.64];

[z,p] = tf2zpk(Numerator,Denominator);

fprintf('Zeros:\n')
disp(z)
fprintf('Poles:\n')
disp(p)

zplane(Numerator,Denominator)
title('Pole-Zero Plot')
grid on

figure

freqz(Numerator,Denominator)
title('Frequency Response')

OUTPUT:

Command Window Zeros: 1.2000 1.2000i 1.2000- 1.2000i Poles: 0.4000 0.6928i 0.4000-0.6928i

Pole-Zero Plot 0.5 0 -0.5 0.5 0.5 1.5 Real Part

Frequency Response 16 14 12 10 8 0.1 0.3 0.5 Normalized Frequencyx rad/sample) 0.2 04 0.6 0.7 08 0.9 -100 3-200 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9 Normalized Frequency (x rad/sample)