plot spectrum of a rectified sine wave without fft but using fourier coefficients in matlab

main.m
% Define the parameters
amplitude = 1;  % Amplitude of the sine wave
frequency = 1;  % Frequency of the sine wave
num_terms = 10; % Number of Fourier coefficients

% Construct the Fourier series for the rectified sine wave
n = 1:num_terms;
an = zeros(1, num_terms);
bn = (2 * amplitude * (-1).^(n-1)) ./ (pi * (2*n - 1));
bn(1) = amplitude / 2;
t = linspace(0, 4*pi, 1000);

% Calculate the spectrum of the rectified sine wave
f = zeros(size(t));
for i = 1:num_terms
    f = f + an(i)*cos((2*pi*(2*i-1)*frequency*t)/(2*pi)) + bn(i)*sin((2*pi*(2*i-1)*frequency*t)/(2*pi));
end

% Plot the spectrum
figure;
plot(t, f);
xlabel('Time');
ylabel('Amplitude');
title('Spectrum of Rectified Sine Wave using Fourier Coefficients');
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