Question

1. (a) Evaluate the Fourier coefficients a, an, ba for the function defined as f)-2 cos() for-π/2 s sn2 and zero else over the period of 2T, do NOT use MATLAB or a calculator for integrations. All the steps should be shown. Write a few terms of the Fourier series expansion Plot 2 or 3 cycles of the Fourier series using MATLAB and verify whether the plot matches the given waveform Find Co and Cn and plot the amplitude spectrum and the phase spectrum of the waveform. (b) (c)

Answer 1

Solution: (a) 2_ 2n ao-2

an 쑤 다 Tt odd'n'

n/レ n+i M- (-リ

Matlab Code for the plot of ft) upto 3 periods clc syms s n t A-2 To=2*pi; % Let fundamental Time Period of the wave is To=2*pi sec. WO-(2*pi/To); %Let fundamental frequency of wave in rad per sec. t 10:0.1:10; ao- (2/pi); al-l; a2-8/ (3*pi); a4e(-4)/(15*pi); %4th harmonic content of 'an' y1-ao+ (al cos (wo*t) y2-yl+ (a2*cos (2*wo*t)) y4-y2+ (a4*cos (4*wo*t)) plot (t,yl,t, y2,t, y4) xlabel('bf time (t) ylabel ('bf Amplitude) title ('bf Fourier Series representation of given wave upto 4 harmonics') grid orn

Fourier Series representation of given wave upto 4 harmonics 2.5 .5 0.5 -0.5 10 -8 .6 .2 10 time(t) Fourier representation of f(t) upto 4th harmonics

2 n-1 J-ude. Co

りぃ. LG Magnitude and Phase Spectrum of 'Cn' 0n