PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

400 Practical MATLAB® Applications for Engineers

Example 4.8

1. Evaluate by hand the FT (non-periodic) of the rectangular pulse f(t) shown in Fig-
   ure 4.49 for the following cases τ = 1, 5, and 10 using the transform pairs provided
   in Table 4.1.


2. Create the script fi le square_FT_num that returns the plots of the FT of part 1 using
   a numerical approach.


3. Create the script fi le square_FT_sym that returns the magnitude spectrum expres-
   sions as well as their plots of the FT of part 1 for different τs using the MATLAB
   symbolic toolbox. Discuss and compare the results obtained.

ANALYTICAL Solution

Part 1

The expression of the FT of f(t) is

(^) ft w
w
()↔


sin( )

2
2
(from Table 4.1)
where τ takes the value of 1, 5, and 10.
MATLAB Solution
% Script file: square FT num
% This file returns the plot of the pulse spectrums for the tau’s=
1,5, and 10
echo off;
w =-10pi:0.1:10pi;
F1 = ones(size(w));
F10 = ones(size(w));
tau1=1;tau5 =5;tau10 = 10;
F1= sin(wtau1/2)./(wtau1/2);
F5 = 5sin(wtau5/2)./(w*tau5/2);
−τ
0.5
f(t)
t
1.0
−τ/2 0 τ/2 τ
FIGURE 4.49
Plot of f(t) of Example 4.8.