Question

Determine the Fourier series for the rectangular wave illustrated in Figure P3.28, and plot the resultsHint:The square wave of period Tis described by

3.27 Determine the Fourier series for the rectangular wave illustrated in Figure P3.28, and plot the results 2T Эт Hint: The square wave of period T is described by

Answer 1

the function is instead defined on the interval, the above equations simply become

[0, 2 L]

here $2L = 2 \pi$

thus   $L = \pi$

$a_{0}=\frac{1}{L} \int_{0}^{2 L} f\left(t\right) d t$

$a_{n}=\frac{1}{L} \int_{0}^{2 L} f\left(t\right) \cos \left(\frac{n \pi t}{L}\right) d t$

$b_{n}=\frac{1}{L} \int_{0}^{2 L} f\left(t\right) \sin \left(\frac{n \pi t}{L}\right) d t$   

(T Fi rT

an 코/T 6 -o o

20 r2

t1t ん

%o f
so the answer is

$fourier \, series =\frac{4}{\pi} \sum_{n=1,3,5, \ldots}^{\infty} \frac{1}{n} \sin \left({n t }\right)$

we shall plot that in Matlab

%plot for fourier series
clc
clear all
t=0:0.1:4*pi;
y1=sin(t)*(4/pi);
y3=sin(t)*(4/pi)+sin(3*t)*(4/(3*pi));
y5=sin(t)*(4/pi)+sin(3*t)*(4/(3*pi))+sin(5*t)*(4/(5*pi));
plot(t,y1,t,y3,t,y5),hold on;
x=square(t);
plot(x,t), hold off;
plot(t,x), hold off;
plot(t,y1,t,y3,t,y5,t,x)
title('fourier series representation')
xlabel('F(t)')
legend('n=1','n=2','n=3','f(t)')

File Edit View Insert Tools Desktop Window Help fourier series representation _ n=1 n-2 n-3 一维) 0.5 -0.5 1.5 10 12 14 F(t)

IF YOU GOT ANY DOUBTS ASK IN COMMENTS SECTION

IF YOU LIKED MY ANSWER PLEASE PROVIDE POSITIVE FEEDBACK