create half-rectified sine plots in time and in frequency with fourier coefficients in matlab

main.m
% Define parameters
f = 1; % Frequency of the sine wave
T = 1; % Time period
fs = 1000; % Sampling frequency
t = 0:1/fs:T; % Time vector
n = 10; % Number of harmonics

% Generate half-rectified sine wave
x = sin(2*pi*f*t);
x(x<0) = 0; % Half rectification

% Plot the half-rectified sine wave in time domain
figure;
subplot(2,1,1);
plot(t, x);
xlabel('Time (s)');
ylabel('Amplitude');
title('Half-Rectified Sine Wave in Time Domain');

% Compute Fourier coefficients
A = zeros(1, n);
B = zeros(1, n);

for k = 1:n
    A(k) = 2/T * trapz(t, x .* cos(2*pi*k*f*t));
    B(k) = 2/T * trapz(t, x .* sin(2*pi*k*f*t));
end

% Generate frequency domain representation
f_axis = (0:n-1)*(f/T);
Xf = A(1)/2 + zeros(size(f_axis)); % DC component

for k = 1:n
    Xf = Xf + A(k)*cos(2*pi*k*f*f_axis*T) + B(k)*sin(2*pi*k*f*f_axis*T);
end

% Plot the Fourier series representation in frequency domain
subplot(2,1,2);
stem(f_axis, abs(Xf));
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('Fourier Series representation of the Half-Rectified Sine Wave');

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