Fourier transform in continuous time signal

The project aims to demonstrate the importance and functionality of Fourier transform in analyzing continuous-time signals.

The project scope includes demonstrating Fourier transform's application in analyzing continuous-time signals. It covers concepts like frequency spectrum, amplitude, and phase. However, it may not delve deeply into advanced topics or specific applications beyond the basics. The focus is on providing a clear and intuitive demonstration of Fourier transform's significance and functionality.

% Define the continuous-time signal
t = -5:0.01:5; % Time vector
x = sin(2*pi*t) + 0.5*cos(4*pi*t); % Example signal

% Compute the Fourier transform
X = fftshift(fft(x));

% Frequency vector
Fs = 1/(t(2)-t(1)); % Sampling frequency
f = linspace(-Fs/2, Fs/2, length(t));

% Plot the original signal
subplot(2,1,1);
plot(t, x);
xlabel('Time (s)');
ylabel('Amplitude');
title('Original Signal');

% Plot the magnitude of the Fourier transform
subplot(2,1,2);
plot(f, abs(X));
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('Fourier Transform');

% Adjusting plot limits for better visualization
xlim([-10, 10]); % Set the frequency range to display