Trigonometric Fourier Series of Even Square Wave

M-file:

% Filename: TrigFSEvenSquareWave.m

% Description: m-file to plot Trigonometric Fourier Series

% representation of even square wave.

clear; clc; close all; % clear memory and command window, close all figures

t = -3:0.001:3; % times as vector over which to plot FS

Nval = [1, 3, 6, 250]; % number of terms for n in four summations

figure(); % open figure in which to plot truncated Fourier Series

for in = 1:4, % % Build four square waves using increasing number of terms

v = 1/2; % initialize sum to a_0 = 1/2

subplot(2,2,in);

% "brute force" plot of true square wave

plot([-3,-5/2,-5/2,-3/2,-3/2,-1/2,-1/2,1/2,1/2,3/2,3/2,5/2,5/2,3], ...

[ 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,0], ...

'k-.','LineWidth',2);

hold on;

for n = 1:Nval(in),

harm = 2*(sin(n*pi/2)/(n*pi))*cos(n*pi*t);

v = v + harm;

plot(t,harm,'b--','LineWidth',1); % plot each harmonic

end

plot(t,v,'r-','LineWidth',2); % plot sum of all terms/harmonics

hold off;

xlabel('time, sec','FontSize',14); ylabel('FS Approx to v(t)','FontSize',14);

title(['Fourier Series Approx w/',num2str(Nval(in)),' Terms'],'FontSize',14);

end

Figure generated: