How to plot this signal x(𝑡) = (𝑡 + 2)𝑢(𝑡 + 2) − 2𝑡𝑢(𝑡) + (2(𝑡 − 4) + 2)𝑢(𝑡 − 4)?

I just am unsure of the correct syntax for plotting a signal with unit step. This is what I have so far. It gives me an error saying incorrect dimensions but I don't know where to put . for multiplying.

clear all; close all; clc;

syms t t0

u(t) = piecewise(t<t0, 0, t>=t0, 1);

t = -10:1:10;

xt = (t+2)*u(t+2)-(2*t*u(t))+((2*(t-4)+2)*u(t-4));

plot(t,xt);

axis([0,40,-2,2])

title('x(t) = (t+2)*u(t+2)-(2*t*u(t))+((2*(t-4)+2)*u(t-4))')

xlabel('t')

ylabel('x(t)')

grid;

Answer 1

[Clayton Gotberg]

One error is in the line

xt = (t+2)*u(t+2)-(2*t*u(t))+((2*(t-4)+2)*u(t-4));

and it is happening because of problems with the size of arrays you're calling. For example, in the first part:

(t+2)*u(t+2)
(t+2) % Adds 2 to each element in t, a 1x21 double
u(t+2) % output of u function on t+2, a 1x21 double
A*B % matrix multiplication - the number of columns in A must equal
% the number of rows in B

When you use *, MATLAB assumes you want matrix multiplication. If you want elements in A to be multiplied by elements in the same place in B, use element-wise multiplication (.*) instead.

To answer your question, anywhere that you want to use element-wise multiplication needs a .* instead of a *

[Clayton Gotberg]

Another problem with your code is that you do not clarify what t0 is, so MATLAB is forced to assume it could be anything.

From what you're doing, my guess is that when you say u(t+2), you want the Heaviside function that is zero for t<2 and one for t>=2. If so, you can either change your function

u(t,t0) = piecewise(t<t0, 0, t>=t0, 1);

or you can change how you are thinking about the function. If you have a function

syms t
time = -10:10;
example(t) = piecewise(t<0, 0, t>=0, 1);

and you call

example(time+2)

you are automatically shifting each value in time by 2, as if you had run

piecewise(time+2<0, 0, time+2>=0, 1);

which is the same as

piecewise(time<-2,0,time>=-2,1);

[Olivia DeBenedictis]

Thank you so much for your help!