Question

Realize signal processing systems described by the difference equation: ?1(?)=1/2 [?(?)+?(?−1)] and ?2(?)=1/2 [?(?)−?(?−1)] using Matlab. Assuming same input signal x(n)=sin(ωn) for various values of ω ={0,p/6 ,3p/2, 1.9p/2} applied to both systems find the following: a. Obtain stem plots and codes of y1(n) and y2(n) in each . b. Critically analyze y1(n) and y2(n) in terms of type of filter, maximum gain and cut off frequency. (Hint : The system can be tested by computing frequency response of the system).

Answer 1

Solution:

Given that

EXECUTABLE CODE:

  

clc;

clear all;

close all;

% first define w

w = [0 pi/6 3*pi/2 1.9*pi/2];

% define n

n = 0:100;

% define system 1 and system 2

num1 = [12 12];

den1 = 1;

num2 = [12 -12];

den2 = 1;

% filtering for various w

for k = 1:length(w)

x = sin(w(k)*n);

% now filter the signal with filter #1

y1 = filter(num1,den1,x);

% now filter the signal with filter #2

y2 = filter(num2,den2,x);

% now plot the filtered signals

figure;

subplot(211);

stem(n,y1);xlabel('n');

title(['filtered signal from system 1 for w = ',num2str(w(k))]);

subplot(212);

stem(n,y2);xlabel('n');

title(['filtered signal from system 2 for w = ',num2str(w(k))]);

end

% Now plot the frequency responses of the filteres

figure;

freqz(num1,den1);grid on;

title('frequency response the filter 1');

figure;

freqz(num2,den2);grid on;

title('frequency response the filter 2');

OUTPUT: