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

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Szalka Gergo
Szalka Gergo 2021-10-24
编辑： Paul 2021-10-25
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.
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Szalka Gergo
Szalka Gergo 2021-10-24
编辑：Szalka Gergo 2021-10-24
Yes, ε(t) should represent the unit step function. I just want to plot y(t), closed form expression is not required.
Paul
Paul 2021-10-24
编辑：Paul 2021-10-25
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)?

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Yongjian Feng
Yongjian Feng 2021-10-24
Do you mean:
  1. create a list of t
  2. compute y for the list of t above
  3. plot(t, y)
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Szalka Gergo
Szalka Gergo 2021-10-24
编辑：Szalka Gergo 2021-10-24
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
Yongjian Feng 2021-10-25
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.

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