 # Consider a pulse signal 𝑥(𝑡) = 𝐴cos(Ω0𝑡)(𝑢(𝑡) &...

## Question

Consider a pulse signal 𝑥(𝑡) = 𝐴cos(Ω0𝑡)(𝑢(𝑡) − 𝑢(𝑡 − 𝜏)).
Generate this signal (its discrete version) using MATLAB for arbitrary constants A (magnitude), Ω0(frequency), and 𝜏 (duration). To illustrate correct functionality of your code, plot the signal 𝑥(𝑡) for a few values of 𝐴, Ω0, and 𝜏.
Evaluate the Fourier transform of 𝑥(𝑡) in MATLAB. Hint: since the signal you generated is actually discrete, you may use, for instance, the 𝑓𝑓t function. Plot magnitude and phase of FT for the same values of 𝐴, Ω0, and 𝜏 that you used before.
What conclusions can you make based on the results you observed? Write a short report with the MATLAB codes you developed and the results you observed. Explain the procedure, discuss the results and conclusions.

## Solution Preview

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%% Clearing screen,workspace and closing all figures
clc;
clear;
close all;
%% Defining different parameter values
%Magnitude
A1 = 5;
A2 = 10;
A3 = 20;
%Frequency
Omega1 = 2*pi*2;
Omega2 = 2*pi*4;
Omega3 = 2*pi*8;
%Duration
Tau1 = 2;
Tau2 = 4;
Tau3 = 8;
%Time step
dt = 0.01;
%Sampling frequency
fs = 1/dt;
%Time vectors
t1 = 0:dt:Tau1;
t2 = 0:dt:Tau2;
t3 = 0:dt:Tau3;...

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