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question 2.10-4 with matlab code.
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the following per
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Answer #1

2.10-4)

a)

clc;close all;clear all;
t=-2:0.01:2
g=(t.^3)
T=4;t1=linspace(-6,6,3*length(t))
g1=[g g g]
subplot(2,2,[1,2])
plot(t1,g1,'r')
xlabel('t')
ylabel('g(t)')
title('Periodic signal g(t)')

%To calculate FFT
fs=1;Ts=1/fs;N=25
n=-N:1:N
g=(n*Ts).^3
G=fft(g);
Gshift=fftshift(G);

subplot(223)
stem(n,(abs(Gshift))/(abs(max(Gshift))))
title('Amplitude spectra')
xlabel('k..>')
ylabel('|G|')
subplot(224)
stem(n,angle(Gshift),'g')
title('Phase spectra')
xlabel('k..>')
ylabel('<G>')

Periodic signal g(t) 10 -5 -10 -6 2 2 4 Amplitude spectra Phase spectra 4 0.8 2 0.6 0.4 -2 0.2 30 20 10 0 10 20 30 30 -20 10

b)

clc;close all;clear all;
t=-1:0.01:3
g=(t>=-1 & t<=1)-(t>=1 &t<=3)
T=4;
t1=linspace(-5,7,3*length(t))
g1=[g g g]
subplot(2,2,[1,2])
plot(t1,g1,'r','linewidth',3)
xlabel('t')
ylabel('g(t)')
title('Periodic signal g(t)')

%To calculate FFT
fs=1;Ts=1/fs;N=25
n=-N:1:N
g=(n>=0 & n<=1)-(n>=3 &n<=5)
G=fft(g);
Gshift=fftshift(G);

subplot(223)
stem(n,(abs(Gshift)))
title('Amplitude spectra')
xlabel('k..>')
ylabel('|G|')
subplot(224)
stem(n,angle(Gshift),'g')
title('Phase spectra')
xlabel('k..>')
ylabel('<G>')

Periodic signal g(t) 0.5 0.5 -6 -4 -2 2 4 Amplitude spectra Phase spectra 4 4 2 3 2 30 20 10 0 10 20 30 30 -20 10 0 10 20 30

c)

clc;close all;clear all;
t=-2:0.01:4
g=((t+2).*(t>=-2 & t<=-1))+(t>-1 &t<=1)+((2-t).*(t>1&t<=2))
T=6;
t1=linspace(-8,10,3*length(t))
g1=[g g g]
subplot(2,2,[1,2])
plot(t1,g1,'r','linewidth',3)
xlabel('t')
ylabel('g(t)')
title('Periodic signal g(t)')

%To calculate FFT
fs=1;Ts=1/fs;N=25
n=-N:1:N
t=n*Ts
g=((t+2).*(t>=-2 & t<=-1))+(t>-1 &t<=1)+((2-t).*(t>1&t<=2))
G=fft(g);
Gshift=fftshift(G);

subplot(223)
stem(n,(abs(Gshift)))
title('Amplitude spectra')
xlabel('k..>')
ylabel('|G|')
subplot(224)
stem(n,angle(Gshift),'g')
title('Phase spectra')
xlabel('k..>')
ylabel('<G>')

Periodic signal g(t) 0.8 F 0.4 0.2 -5 10 -10 Amplitude spectra Phase spectra 3 4 2.5 2 2 1.5 0.5 30 20 10 0 10 20 30 30 -20 1

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