Hello Mona,
To compute and plot the amplitude and phase of a signal after performing its Fourier transform in MATLAB, you can follow these steps. I'll guide you through the process for both the Gaussian function 
and the sum of two exponential functions 
.
and the sum of two exponential functions .Fourier Transform of 
First, let's compute and plot the amplitude and phase of the Fourier transform of 
.
.syms t w
% Define the function
x = exp(-t^2);
% Compute the Fourier Transform
X = fourier(x, t, w);
% Substitute '2*pi*f' with 'w' if needed (in this case, it's already in terms of 'w')
% Xf = subs(X, '2*pi*f', 'w'); % Not necessary here
% Define frequency range for plotting
w_vals = linspace(-10, 10, 1000);
% Evaluate the Fourier Transform
X_vals = double(subs(X, w, w_vals));
% Compute amplitude and phase
amplitude = abs(X_vals);
phase = angle(X_vals);
% Plot amplitude
figure;
subplot(2, 1, 1);
plot(w_vals, amplitude);
title('Amplitude Spectrum');
xlabel('Frequency (rad/s)');
ylabel('Amplitude');
% Plot phase
subplot(2, 1, 2);
plot(w_vals, phase);
title('Phase Spectrum');
xlabel('Frequency (rad/s)');
ylabel('Phase (radians)');
Fourier Transform of 
For this part, we need to include the unit step function 
, which can be represented in MATLAB using the heaviside function.
, which can be represented in MATLAB using the heaviside function.syms t w
% Define the function with unit step
x = (exp(-3*t) + exp(-2*t)) * heaviside(t);
% Compute the Fourier Transform
X = fourier(x, t, w);
% Define frequency range for plotting
w_vals = linspace(-10, 10, 1000);
% Evaluate the Fourier Transform
X_vals = double(subs(X, w, w_vals));
% Compute amplitude and phase
amplitude = abs(X_vals);
phase = angle(X_vals);
% Plot amplitude
figure;
subplot(2, 1, 1);
plot(w_vals, amplitude);
title('Amplitude Spectrum of (e^{-3t} + e^{-2t})u(t)');
xlabel('Frequency (rad/s)');
ylabel('Amplitude');
% Plot phase
subplot(2, 1, 2);
plot(w_vals, phase);
title('Phase Spectrum of (e^{-3t} + e^{-2t})u(t)');
xlabel('Frequency (rad/s)');
ylabel('Phase (radians)');
I hope this helps!
