Question

2.7-1 (a) Sketch the signal g(t) = 12 and find the exponential Fourier series to represent 8(1) over the interval (-1, 1). Sketch the Fourier series p(i) for all values of 1.
solve it using matlab

Answer 1

MATLAB:

clc;
clear all;
close all;

%Define g(t)
tt=-1:0.001:1;T=3
gg=(tt.^2).*(tt>=-1&tt<=1)
t=linspace(-T,T,3*length(tt))
g=[gg gg gg];
subplot(211)
plot(t,g,'linewidth',3,'b');grid;xlabel('t');
ylabel('g(t)');title('g(t)=t^2');

%Exponential fourier series
T0=2;w0=2*pi/T0;N=5;
k=0;
for n=-N:1:N
k=k+1;
c(k)=(trapz(tt,gg.*exp(-j*n*w0*tt)));
end
c=c/T0

%To plot fourier series of g(t)
k=0;n=-N:1:N
for t=t
k=k+1;
gN(k)=sum(c.*(exp(j*n*w0*t)));
end
t=linspace(-T,T,3*length(tt))
subplot(212)
plot(t,gN,'m','linewidth',3)
title('Fourier series approximation of g(t)')
xlabel('t')
ylabel('gN(t)')
grid on;

Plot:

g(t)=42 (1)6 2 Fourier series approximation of g(t) gN(t)

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