Demo of the Fourier Series

fourier_approx.m

%% Remove items from workspace
clear;

%% Interval of x
x = linspace(-10, 10, 10000);

%% Example 1
orig = x;
a_0 = 0;
a_k = @(k) 0;
b_k = @(k) (-1)^(k + 1) * 2 / k;

%% Example 2
% orig = pi .* (x <= 0) + 2 .* x .* (x > 0);
% a_0 = pi;
% a_k = @(k) 2  * ((-1)^k - 1) / (pi * k^2);
% b_k = @(k) (-1 - (-1)^k) / k;

%% Degree of trigonometric polynomial
% k = 1;
% k = 5;
% k = 10;
% k = 100;
k = 1000;

%% Main function
appx_degree = @(k, x) a_k(k) * cos(k * x) + b_k(k) * sin(k * x);
appx = ones(size(x)) * a_0;
for i = 1:k
    appx = appx + appx_degree(i, x);
end

%% Set x-axis limits 
xlim([-pi pi]);
% xlim([(-2 * pi) (2 * pi)]);
% xlim([(-3 * pi) (3 * pi)]);

%% Plotting section
hold on;
grid on;

plot(x, orig, x, appx);

lgnd = ["origin" ("approx. n = " + int2str(k))];
legend(lgnd);

hold off;