% Define the time vector
t = 0:0.01:2*pi;  % from 0 to 2*pi with increments of 0.01

% Define the function, a sine wave in this case
f = sin(2 * pi * 5 * t);  % 5 Hz sine wave

% Plot the original function
figure;
subplot(2,1,1);
plot(t, f);
title('Original Function: 5 Hz Sine Wave');
xlabel('Time');
ylabel('Amplitude');

% Compute the Fourier Transform
F = fft(f);

% Frequency vector
n = length(t); % number of samples
freq = (0:n-1)*(1/(n*0.01)); % frequency range

% Plot the Fourier Transform (magnitude)
subplot(2,1,2);
plot(freq, abs(F));
title('Fourier Transform');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
xlim([0 20]); % limit x-axis to 20 Hz for better visualization
x = -pi:0.1:pi;
plot(x, cos(x))