create graph of a half-wave rectified sine in time and in frequency without using fft in matlab

main.m
% Define the parameters
f = 1;                  % Frequency of the sine wave (Hz)
A = 1;                  % Amplitude of the sine wave
t = 0:0.001:1;          % Time vector from 0 to 1 second with a step size of 0.001 seconds

% Create the half-wave rectified sine wave in the time domain
x = A*sin(2*pi*f*t);
rectified_x = max(x, 0);

% Plot the half-wave rectified sine wave in the time domain
figure;
subplot(2, 1, 1);
plot(t, x, 'b', 'LineWidth', 1.5);
title('Half-Wave Rectified Sine Wave in Time Domain');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 1, 2);
plot(t, rectified_x, 'r', 'LineWidth', 1.5);
title('Half-Wave Rectified Sine Wave in Time Domain after Rectification');
xlabel('Time (s)');
ylabel('Amplitude');

% Perform Fourier series analysis to obtain the frequency domain representation
N = 10;                 % Number of harmonics to consider
frequencies = 0:N;      % Frequencies to analyze

% Calculate the Fourier series coefficients
an = zeros(size(frequencies));
bn = (2*A/pi)./(1:2:2*N)*(-1).^(floor((1:2:2*N)/2));
bn(2:2:end) = 0;  % Odd harmonics only as we are dealing with a half-wave rectified signal

% Reconstruct the signal in frequency domain using computed coefficients
frequency_x = A/2;  % DC component (fundamental frequency)
for k = 1:N
    frequency_x = frequency_x + an(k)*cos(2*pi*k*f*t) + bn(k)*sin(2*pi*k*f*t);
end

% Plot the half-wave rectified sine wave in the frequency domain
figure;
plot(t, rectified_x, 'r', 'LineWidth', 1.5);
title('Half-Wave Rectified Sine Wave in Frequency Domain (Fourier Series Approximation)');
xlabel('Time (s)');
ylabel('Amplitude');
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