Question

1. Use the MATLAB command freqz to calculate the DTFT of System 1, to find its frequency response 0.25r[n] + 0.25r|n -2]. H(). For this exercise, System 1 has a different difference equation yn] Find H1 (w) for- aK π, with frequency steps of Δα-π/100. 2. Plot both the magnitude |H1(2)| and the phase LH1(w) vs w, for-π < ώ < π. Use abs and angle commands to obtain magnitude and phase. Label and title both plots and include in your lab report 3. Use the MATLAB command freqz to calculate the DTFT of System 2, to find its frequency response H2(a). System 2 is the scaled 3-point moving average filter with impulse response H2[n-δ1n] + δ[n-1] + δ[n-2]. Find H2(4) for π SO T, with frequency steps of Δ-T/ 100. 4. Plot both the magnitude |H2(a) l and the phase LH2(2) vs w, for-π < ω < π. Label and title both plots and include in your lab report.

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all

% questions 1 and 2
% define the numerator and denominator coefficients
numerator = [0.25 0 0.25];
denominator = 1;
% define the frequency resolution
del_w = pi/100;
%define the frequency vector
w = -pi:del_w/pi:pi;
% now compute the frequency reponse using the command
H1 = freqz(numerator,denominator,w);

% plot the frequency repsonse as given below
% use subplots for magnitude and phase
figure;
subplot(211);
plot(w,abs(H1),'linewidth',2);grid on;xlabel('w');ylabel('Amplitude');
title('magnitude response of system #1 |H_1(exp(jw))|');

subplot(212);
plot(w,angle(H1)*57.3,'linewidth',2);grid on;xlabel('w');ylabel('Degrees');
title('phase response of system #1 ');

% questions 3 and 4 for system #2
% define the numerator and denominator coefficients
numerator = [1 1 1];
denominator = 1;
% define the frequency resolution
del_w = pi/100;
%define the frequency vector
w = -pi:del_w/pi:pi;
% now compute the frequency reponse using the command
H2 = freqz(numerator,denominator,w);

% plot the frequency repsonse as given below
% use subplots for magnitude and phase
figure;
subplot(211);
plot(w,abs(H2),'linewidth',2);grid on;xlabel('w');ylabel('Amplitude');
title('magnitude response of system #2 |H_2(exp(jw))|');

subplot(212);
plot(w,angle(H2)*57.3,'linewidth',2);grid on;xlabel('w');ylabel('Degrees');
title('phase responseof system #2 ');

magnitude response of system #1/H,(exp(jw) 0.6 0.4 0.2 -3 2 phase response of system #1 100 50 -50 -100 -3 -2 2

magnitude response of system #2]H,(exp(jw) -3 2 phase response°f system #2 100 50 -50 -100 -3 -2 2