Question

in MATLAB plot the following

EXAMPLE 4.2 Fourier series of a square wave Consider the square wave of Figure 4.4. This signal is common in physical systems. For ex- ample, this signal appears in many electronic oscillators as an intermediate step in the gener ation of a sinusoid We now calculate the Fourier coefficients of the square wave. Because V, 0< t < To/2 x(t) = from (4.23), it follows that ToJTo2 To/2 - e ikast To/2 The values at the limits are evaluated as 2T To Therefore, x(t) 0 To/2 3To2 Figure 4.4 Square wave with amplitude V.

Answer 1

2. KTT k-even

2V 2 V ートJ丿 2 2.V

Code:

clc;clear all;close all;
t=0:0.1:4*pi;
y1=sin(t)*(2/pi);
y3=sin(t)*(2/pi)+sin(3*t)*(2/(3*pi));
y5=sin(t)*(2/pi)+sin(3*t)*(2/(3*pi))+sin(5*t)*(2/(5*pi));
y7=sin(t)*(2/pi)+sin(3*t)*(2/(3*pi))+sin(5*t)*(2/(5*pi))+sin(7*t)*(2/(7*pi));
plot(t,y1,t,y3,t,y5,t,y7),hold on;
x=square(t);
%plot(x,t),hold off;
plot(t,x),hold off;
plot(t,y1,t,y3,t,y5,t,y7,t,x)
%grid on
legend('n=1','n=3','n=5','n=7','f(t)')

MATLAB FOUIRER SERIES REPRESENTATION:

n-1 0.2 0.6 0.8 10 12