Finding the impulse response of a system

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Homework Statement


So the problem asks to find the impulse response h(t) provided y(t) = integral from -infinity to t of e^-(t-tau)*x(tau-2)dtau


Homework Equations


none



The Attempt at a Solution


I understand that the way to begin this problem is to substitute delta(t) for x(t). Therefore the equation becomes y(t) = integral from -infinity to t of e^-(t-tau)*delta(tau-2)dtau

However, at this point I am unsure of how to begin solving the integral.

Thanks for any help.
 

Answers and Replies

  • #2
vela
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The basic relationship for the Dirac delta function is

[tex]\int_{-\infty}^\infty f(x)\delta(x-x_0)\,dx = f(x_0)[/tex]

It picks out the value of the function f(x) when the argument of delta function is 0.
 
  • #3
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I understand the concept of the delta function. However, I am having trouble manipulating the integral. Each time I try something I achieve h(t) equal to a constant which is not correct at all. h(t) should be in terms of t.
 
  • #4
vela
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Show your work. I have no idea how you are managing to get a constant.
 

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