How to plot output y(t) of LTI system, where impulse response h(t) and input x(t) are given?

I would like to determine and plot a LTI system's output [ y(t) ] .

I know that y(t) can be determined by convolving input and impulse response, or y(t) = x(t) * h(t), but I can't figure out how to plot output correctly.

[Paul]

Does epsilon(t) in the definition of h(t) represent the unit step function? If so, should that term alos be included in the definition of x(t)?

Are you trying to get closed form expression for y(t) or just a plot of an approximation of y(t)?

[Szalka Gergo]

Yes, ε(t) should represent the unit step function. I just want to plot y(t), closed form expression is not required.

[Paul]

x(t) does not include that term ε(t) . So as written x(t) is non-zero for t < 0. Is that the correct interpretation of x(t)?

Answer 1

[Yongjian Feng]

Do you mean:

1. create a list of t
2. compute y for the list of t above
3. plot(t, y)

[Szalka Gergo]

Yes, definitely. I wrote a new code, but I'm not sure if it's good...

t=linspace(0,10,100);
h=4 * exp(-t);     % imp. response : h(t) = 4ε(t)e^-t 
x=8 * exp(2*t);    % input : x(t) = 8e^2t
y=conv(h,x);
figure
subplot(3,1,1)
plot(t,h); title h(t)
subplot(3,1,2)
plot(t,x); title x(t)
subplot(3,1,3)
plot(t,y(1:100)) ; title y(t)

Figure:

[Yongjian Feng]

Well one way to verify is to pick several points of t, compute x(t), h(t) and y(t) by hand (or say use a calculator). Then verify y(t) on the figure is correct.