amplitude spectrum of signal

1)Determine and plot the amplitude spectrum of the even signal x(t) analytically and numerically, then compare the results.

2)If signal x(t) passes through an LTI system with impulse response h(t); Determine and plot the amplitude and phase spectrum of the output signal.

Answer 1

[Anudeep Kumar]

Hey @AshCrow,

You can define 'x(t)' and 'h(t)' using basic MATLAB arrays as below and plot using the 'plot()' function.

% Define t
t = -5:0.01:5; % Adjust the range and step as needed

% x(t)
x = zeros(size(t));
x(abs(t) >= 0 & abs(t) <= 1) = t(abs(t) >= 0 & abs(t) <= 1) + 1;
x(abs(t) > 1 & abs(t) <= 2) = 2;
x(abs(t) > 2 & abs(t) <= 4) = -t(abs(t) > 2 & abs(t) <= 4) + 4;

% h(t)
h = zeros(size(t));
h(t >= 0 & t <= 2) = 1;
h(t > 2 & t <= 3) = -1;

% Plot x(t)
figure;
subplot(2,1,1);
plot(t, x, 'LineWidth', 2);
xlabel('t'); ylabel('x(t)');
title('x(t)');
grid on;

% Plot h(t)
subplot(2,1,2);
plot(t, h, 'LineWidth', 2);
xlabel('t'); ylabel('h(t)');
title('h(t)');
grid on;

As for the second part please look into the 'conv' function from MATLAB and apply it as per your use case. Below are the links to all the documentation you may want to refer to:

https://www.mathworks.com/help/releases/R2024b/matlab/ref/conv.html

https://www.mathworks.com/help/releases/R2024b/matlab/ref/plot.html

I hope this helps!