gibbs phenomena in matlab

main.m
T = 1;  % period of the square wave
t = linspace(0, 4*T, 1000);  % time vector
square_wave = @(t) sign(sin(2*pi*t/T));
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main.m
figure;
plot(t, square_wave(t));
title('Square Wave');
xlabel('Time');
ylabel('Amplitude');
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main.m
n = 50;  % number of terms in the Fourier series
approximation = zeros(size(t));
for k = 1:n
    coefficient = 4/pi * sin(2*pi*k*t/T) / k;
    approximation = approximation + coefficient;
end
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main.m
figure;
plot(t, approximation);
title('Approximation using Fourier series');
xlabel('Time');
ylabel('Amplitude');
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main.m
figure;
plot(t, square_wave(t) - approximation);
title('Gibbs Phenomenon');
xlabel('Time');
ylabel('Difference');
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