fourier coefficient of a rectified sine wave in matlab

main.m
% Define the rectified sine wave function
Fs = 1000;                      % Sampling frequency
t = 0:1/Fs:1;                   % Time vector
f = 5;                          % Frequency of the sine wave
x = abs(sin(2*pi*f*t));         % Rectified sine wave

N = length(x);                  % Length of the signal
X = fft(x)/N;                   % Compute the Fourier coefficients

% Frequency vector
frequencies = 0:Fs/N:Fs/2;

% Plot the magnitude spectrum
plot(frequencies, abs(X(1:N/2+1));
title('Magnitude Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude');

% Find the relevant Fourier coefficients
% Index corresponding to the frequency of the sine wave
index = find(frequencies == f);
coeff_sine = X(index+1);        % Coefficient corresponding to the sin(2*pi*f*t) term

% Display the coefficient
disp(['Fourier coefficient of the sine wave: ', num2str(coeff_sine)]);
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