Question

The purpose of this problem is to become familiar with the use of MATLAB. Consider the continuous-time function x(t) 2e0.5sin(87t)u(t), where u(t) is the unit step function. a) (10 points) Design a MATLAB routine to plot x(t) from t -5 to t = 5 using 10, 100, and 1000 equally spaced samples. The following MATLAB code fragment suggests how this 11. can be done (using 1000 equally spaced samples). Note that the function provided by MATLAB, but can be easily generated using the sign) unit_step() is not and abs() functions. Turn in a listing of the code you used to accomplish this, along with plots of x(t). Label your plot using the title(), xlabel) and ylabel() functions. Comment on the difference between the three plots. t (-5:0.01:5) x-2*exp(-0.5*t)*sin(8**t)*unit_step(t) plot(t,x) b) (10 points) Design a MATLAB routine to plot the following functions. Turn in a listing of the code used to accomplish this, along with appropriately labeled printouts of each of the functions. (For each function, you will need to choose a range of time and sample spacing that allows the behavior to be clearly For each function, give a brief explanation for how the function relates to x(t), such as "shifted to the left by 12". seen from your printout.)

Answer 1

MATLAB code is given below in bold letters.

clc;
clear all; % clear all variables
close all;

% define the time vector with 10 equally spaced samples
t = linspace(-5,5,10);

% define the unit step function
unit_step = (t>=0); % when time is > = 0 the logical values one is set.

% define the signal itelf
x = 2 * exp(-0.5*t) .* sin(8*pi*t) .* unit_step; % .* is used for point wise vector multiplication

% now plot the signal with 10 equally spaced points
figure;
plot(t,x);grid on;
xlabel('time(s)');ylabel('Amplitude');
title('x(t) with 10 equally spaced points');

clear all; % clear all variables

% define the time vector with 100 equally spaced samples
t = linspace(-5,5,100);

% define the unit step function
unit_step = (t>=0); % when time is > = 0 the logical values one is set.

% define the signal itelf
x = 2 * exp(-0.5*t) .* sin(8*pi*t) .* unit_step; % .* is used for point wise vector multiplication

% now plot the signal with 10 equally spaced points
figure;
plot(t,x);grid on;
xlabel('time(s)');ylabel('Amplitude');
title('x(t) with 100 equally spaced points');

clear all; % clear all variables

% define the time vector with 1000 equally spaced samples
t = linspace(-5,5,1000);

% define the unit step function
unit_step = (t>=0); % when time is > = 0 the logical values one is set.

% define the signal itelf
x = 2 * exp(-0.5*t) .* sin(8*pi*t) .* unit_step; % .* is used for point wise vector multiplication

% now plot the signal with 10 equally spaced points
figure;
plot(t,x);grid on;
xlabel('time(s)');ylabel('Amplitude');
title('x(t) with 100 equally spaced points');

x(t) with 10 equally spaced points 1.5 1 0.5 0 -0.5 -1 -5 5 4 2 -2 -4 time(s) N LO LC LO Amplitude

x(t) with 100 equally spaced points 2 1.5 0.5 0 -0.5 -1 -1.5 -5 -4 -2 2 4 5 time(s) Amplitude LC

x(t) with 1000 equally spaced points 2 1.5 1 0.5 0 -0.5 -1.5 5 4 2 -2 -5 -4 time(s) Amplitude N

From the above plots, it is observed that the first figure is not a good reproduction of the signal. This is because of the fact that the sampling frequeny is not sufficiently enough for reproducing all the frequency components of the signal. In the secondd figure, the signal severely distorted because of the less sampling freuency. The third plot is a best reproduction of the orignal signal. this is because the sampling frequency is much higher than the maximum frequency component of the signal.