function testfourier
% PRE:  -
% POST: Plots the Fourier series of the two functions as
%       specified on the exercise sheet.

% Implementation of the given functions:

% One instance of f:
f1 = @(t) abs(t).*(+(and(-0.5 <= t,t < 0.5)));
% Periodized version:
f = @(t) f1(t)+f1(t-1)+f1(t+1)+f1(t-2)+f1(t+2);
% One instance of g:
g1 = @(t) -(and(-0.5<t,t<0))+(and(t>0,t<0.5));
% Periodized version:
g = @(t) g1(t)+g1(t-1)+g1(t+1)+g1(t-2)+g1(t+2);

% For plotting:
xx = linspace(-2,2,1e4);
yy = f(xx);
zz = g(xx);

% Calculating the Fourier series:
ff = 0.25*ones(size(xx));
gg = zeros(size(xx));
for k=1:19
    ff = ff + ((-1)^k-1)./pi^2/k^2*cos(2*pi*k*xx);
    gg = gg + 2*(1-(-1)^k)/pi/k*sin(2*pi*k*xx);
    if (k==1)
        f1 = ff;
        g1 = gg;
    elseif (k==3)
        f3 = ff;
        g3 = gg;
    elseif (k==5)
        f5 = ff;
        g5 = gg;
    end
end

% Plotting
plot(xx,yy,'k--',xx,f1,xx,f3,xx,f5,xx,ff);
title('Fourier Series of f(t)');
xlabel('t'); ylabel('S_nf(t)');
legend('f','n=1','n=3','n=5','n=19');

figure;
plot(xx,zz,'k--',xx,g1,xx,g3,xx,g5,xx,gg);
title('Fourier Series of g(t)');
xlabel('t'); ylabel('S_ng(t)');
legend('f','n=1','n=3','n=5','n=19');