Question

Use MATLAB to answer the following questions: PARTA Both of these signals were sampled uniform sampling of 1 second duration, xi(n) = cos [21(0.2)t] and x2(n)= cos [2(1.2)t] 1) show results of sampling both signals 2) comments on the results and explain your statements. PART B Both of these signals were sampled uniform sampling of 1 second duration, x(n) = cos [29(0.2)t] and x2(n)= cos [2A(.8)t] 1) show results of sampling both signals 2) comments on the results and explain your statements. PARTC Explain the problems in each part and explain the difference between part 1 and part 2.

Answer 1

MATLAB code for parts A ans B is given below. MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% PART A

% define sampling time Ts = 1;
Ts = 1;

% define time vector for 20 seconds
t = 0:Ts:20;

% define x1[n]
x1 = cos(2*pi*0.2*t);

% plot the signal
figure;
stem(t,x1,'fill');grid on;
xlabel('time');ylabel('Amplitude');
title('x1[n] = cos(2\pi(.2)t');ylim([-1.2 1.2]);

% define x2[n]
x2 = cos(2*pi*1.2*t);

% plot the signal
figure;
stem(t,x2,'fill');grid on;
xlabel('time');ylabel('Amplitude');
title('x2[n] = cos(2\pi(1.2)t');ylim([-1.2 1.2]);

% PART B

% define sampling time Ts = 1;
Ts = 1;

% define time vector for 20 seconds
t = 0:Ts:20;

% define x1[n]
x1 = cos(2*pi*0.2*t);

% plot the signal
figure;
stem(t,x1,'fill');grid on;
xlabel('time');ylabel('Amplitude');
title('x1[n] = cos(2\pi(.2)t');ylim([-1.2 1.2]);

% define x2[n]
x2 = cos(2*pi*0.8*t);

% plot the signal
figure;
stem(t,x2,'fill');grid on;
xlabel('time');ylabel('Amplitude');
title('x2[n] = cos(2\pi(.8)t');ylim([-1.2 1.2]);

PART A: The signals are plotted below.

x1[n] COS(2(-2) 1 0.8 HA 0.6 0.4 0.2 Amplitude 0 -0.2 -0.4 -0.6 -0.8 0 4 6 8 12 14 16 18 20 N 10 time

X2[n] = cos(24(1.2) 1 0.8 HA 0.6 0.4 0.2 Amplitude 0 -0.2 -0.4 -0.6 -0.8 0 4 6 8 12 14 16 18 20 N 10 time

PART B:

x1[n] COS(2(-2) 1 0.8 HA 0.6 0.4 0.2 Amplitude 0 -0.2 -0.4 -0.6 -0.8 0 4 6 8 12 14 16 18 20 N 10 time

x2[n] = cos(21(-8) 1 0.8 HA 0.6 0.4 0.2 Amplitude 0 -0.2 -0.4 -0.6 -0.8 0 4 6 8 12 14 16 18 20 N 10 time

PART C:

For part A, It is observed that the signals x1[n] ans x2[n] look the same. It is because that the sampling frequency of the signals is not sufficient for the component of 1.2 Hz while it is sufficient for 0.2 Hz component. The sampling frequency required for 1.2 Hz component is 2.6 Hz while the given sampling frequency is 1 Hz.

For part B, It is observed that the signals x1[n] ans x2[n] look the same. It is because that the sampling frequency of the signals is not sufficient for the component of 0.8 Hz while it is sufficient for 0.2 Hz component.The sampling frequency required for 0.8 Hz component is 1.6 Hz while the given sampling frequency is 1 Hz.