plot spectrum of a rectified sine wave without fft in matlab

main.m
% Define parameters
Fs = 1000; % sampling frequency
t = 0:1/Fs:1; % time vector
f = 5; % frequency of the sine wave
A = 2; % amplitude of the sine wave

% Generate rectified sine wave
y = abs(A*sin(2*pi*f*t));

% Compute Discrete Cosine Transform
N = length(y); % length of signal
n = 0:N-1;
k = 0:N-1;
DCT_matrix = sqrt(2/N) * cos(pi/N * (n' + 0.5) * k);
spectrum = DCT_matrix * y';

% Plot spectrum
stem(k, spectrum);
xlabel('Frequency (k)');
ylabel('Magnitude');
title('Spectrum of Rectified Sine Wave without FFT using DCT');
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