Question

3. For the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, “main” means having at least 2% of the amplitude of the fundamental harmonic. Use MATLAB to plot the signal for two pFor the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, main means having at least 2% of the amplitude of the fundamental harmonic. Use MATLAB to plot the signal for two periods. Also plot approximations to the signal using finitely many harmonics r(t) 1 23 4 5 6 7 8eriods. Also plot approximations to the signal using finitely many harmonics..

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Answer #1

Consider the signal x(r) The signal repeats for every 3 seconds Thus, the time period Tis 3 sec Define the signal -0 2<t<3 De

2π 2Tn 2πη Sih ATn sin+COS The Fourier series is, 2770s(2m)-1 2mn 2722 Sin-t , cos The fundamental harmonics are obtained by

Determine the main harmonics 4π 8T 47 8r 3 ) 2π 4π 87 sin_t 87323 = 1-0019 + 0.1378 +0.038 cos 0.0329 +0.157 sint -1+ 2π 2T f

1.2 0.8 0.6 0.4 0.2 4 a0-0.5; ft-a0 t 0:0.001:6,; for n-1: 1000 an (3./ (2.*pi*n.*2)) . *cos (2*pi*n/3) (1/ (pi*n)) . *sin (4

MATLAB code:

function f=sig(t)

if t<=1

    f=t;

elseif t<=2

    f=1;

elseif t<=3

   f=0;

elseif t<=4

    f=t-3;

elseif t<=5

    f=1;

else

   f=0;

end

fplot(@sig,[0 6])

xlabel t

ylabel x(t)

---------------

a0=0.5;

ft=a0;

t=0:0.001:6;

for n=1:1000

an=(3./(2.*pi*n.^2)).*cos(2*pi*n/3)+(1/(pi*n)).*sin(4.*pi.*n/3)-3/(2.*pi.^2*n.^2);

bn=(3./(2.*pi.^2.*n.^2)).*sin(2.*pi.*n./3)+(1./(pi.*n)).*cos(4.*pi.*n./3);

ft=ft+an.*cos(n.*2.*pi.*t./3)+bn.*sin(n.*2.*pi.*t./3);

end

plot(t,ft)

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