Question

Sketch the following in Matlab

x(t) = 4(t + 2)u(t + 2) - 4tu(t) - 4u(t - 2) - 4(t - 4)u(t - 4) + 4(t - 5)u(t - 5)

Sketch x(2t - 4)

Answer 1

% First we need t create a time vector t
t = -3:0.001:6;
u = @(t) t>=0; % creating unit step response

% Defining the function x(t)
x = @(t) 4*(t+2).*u(t+2) - 4*t.*u(t) - 4*u(t-2) -4*(t-4).*u(t-4) + 4*(t-5).*u(t-5);

figure; % Plotting the signals as subplots in a graph
subplot(211);plot(t,x(t),'linewidth',2);
grid on; grid minor;
title('x(t)');ylim([-2 10]);
subplot(212);plot(t,x(2*t-4),'linewidth',2);
grid on; grid minor;
title('x(2t-4)');ylim([-2 10]);