Matlab Code below:

% script to compute and plot the frequency spectrum for

% the Fourier series coefficients for f(t)

% Reference: Advanced Engineering Mathematics with MATLAB

% by Dean Duffy

n = 20; % number of harmonics

an = zeros(n,1);

bn = zeros(n,1);

% compute the Fourier coefficients an and bn

% the coefficients in this example are obtained from the

% Fourier series expansion for

% f(t) = 0, -pi

% t, 0

for i = 1:n

% an(i) = 1/i^2/pi*((-1)^i - 1);

% bn(i) = (-1)^(i+1)/i;

an(i) = 2*(-1)^i/i^2;

bn(i) = (-1)^(i+1)*pi/i + 2/pi/i^3*(-1)^i - 2/pi/i^3;

end

% compute the magnitude

cn = 0.5*sqrt(an.*an + bn.*bn);

% incorporate a0

cn = [pi*pi/3; cn];

harmonics = [0; (1:1:20)'];

% plot the spectrum

axes('FontSize',20) % set the font size

stem(harmonics, cn, 'filled') % plot spectrum as a stem plot

set (gca, 'PlotBoxAspectRatio', [8 4 1]) % set aspect ratio

xlabel('harmonics') % label x axis

ylabel('(a_n^2 + b_n^2)^{1/2}/2') % label y axis

title('Plot of Frequency Spectrum for f(t) = 0, -\pi 4. (6 pts.) Compute and plot the Fourier series expansion for the 27 periodic function I t?, T 0, -a