Finding the impulse response of a system

[btse]

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.

 

[vela]

The basic relationship for the Dirac delta function is

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

It picks out the value of the function f(x) when the argument of delta function is 0.

 

[btse]

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.

 

[vela]

Show your work. I have no idea how you are managing to get a constant.