# Finding the impulse response of a system

## 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

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.

Related Engineering and Comp Sci Homework Help News on Phys.org
vela
Staff Emeritus
Homework Helper
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.

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
Staff Emeritus