clc;
clear all;
close all;
% Define time vector
t = 0:0.016:1;
% Define parameters for the triangular wave
a = 10;
% Amplitude
f = 50;
w = 0.6;
% Frequency in Hz
% Duty cycle (0.5 for symmetrical triangular wave)
y = a*sawtooth(2*pi*f*t, w); % Generate triangular wave
% Plot the triangular wave
figure;
subplot(2,1,1);
plot(t, y, 'r');
axis([0 1 -3 3]);
xlabel('Time in seconds');
ylabel('Amplitude');
title('Triangular Wave');
% Fourier Series Approximation
T = 1/f; % Period of the signal
N = 10; % Number of terms in the Fourier Series
f_approx = zeros(size(t)); % Initialize Fourier series approximation
% Fourier Series Approximation using numerical integration (trapz)
for n = 1:N
% Calculate Fourier coefficients a_n and b_n using numerical integration (trapz)
an = (2/T) * trapz(t, y .* cos(2*pi*n*f*t)); % Fourier coefficient for cos term
bn = (2/T) * trapz(t, y .* sin(2*pi*n*f*t)); % Fourier coefficient for sin term
% Add terms to the Fourier series approximation                  f_approx = f_approx + an * cos(2*pi*n*f*t) + bn * sin(2*pi*n*f*t);
end
% Plot Fourier Series approximation
subplot(2,1,2);
plot(t, y, 'b', t, f_approx, 'm');
legend('Original Triangular Wave', 'Fourier Series Approximation');
xlabel('Time in seconds');
ylabel('Amplitude');
title('Fourier Series Approximation to Triangular Wave');

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