PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 397

Create the script fi le Fourier_ approx that returns the following:

1. The plots of the approximation for f(t) using the fi rst 26, 11, and 4 terms of the
   trigonometric FS, over the range − 3 ≤ t ≤ +3.


2. For each of the approximation plots of part 1, evaluate the values of f(t) at t = 0
   and 0.1.


3. Plot the four-term trigonometric FS approximation over the range 1 ≤ t ≤ 2, with
   and without the help of a Hamming window, and observe the effects of the window-
   ing process.

MATLAB Solution

%Script file : Fourier _ approx

echo off ;

t =−3:0.1:3;

x25=0;

for n=1:1:25;

xn25=1/(pi*n)*sin(2*pi*n*t);

x25=x25+xn25; % sum of 25 terms

end;

ft26=0.5+x25; % add the DC

figure(1)

subplot(3,1,1);plot(t,ft26)

title('26 term approximation ')

ylabel('Amplitude')

x10=0;

for n=1:1:10;

xn10=1/(pi*n)*sin(2*pi*n*t);

x10=x10+xn10; % sum of 10 terms

end;

x3=0;

for n=1:1:3;

xn3 =1/(pi*n)*sin(2*pi*n*t);

x3 = x3+xn3; % sum of 3 terms

end;

ft4 = 0.5+x3; % add DC

ft11 = 0.5+x10;

subplot(3,1,2);plot(t,ft11);

ylabel('Amplitude');

title('11 term approximation ')

subplot(3,1,3);

plot(t,ft4);ylabel('Amplitude')

0

t (s)

f(t)

1

1

T=1

FIGURE 4.46

Plot of f(t) of Example 4.7.