# Convolution Homework Involving Impulse Functions

1. Apr 13, 2012

### martnll2

1. The problem statement, all variables and given/known data

How do you do a convolution of two functions containing only impulses?

2. Relevant equations

Say you have 2 functions to convolve, f1 and f2.
I can't do the impulse symbol, so lets call it q.

Say f1 = 2q(t+1) + 2q(t-4) and f2 = q(t-3)

What is f1 convolved with f2? Or how do you do it?

f(t) convolved with y(t) = h(t)
F(w)Y(w) = H(w)

3. The attempt at a solution

So I thought the way to do this is to just add the two functions together, but I am unsure.

2. Apr 13, 2012

### RoshanBBQ

Do you know the impulse sampling rule? Let a(t) be another impulse. It works the same way. Set up the integrals for convolution and use this rule as needed.
$$\int\limits_{-\infty}^{\infty} \delta(t-t_0)a(t)dt=a(t_0)$$
More generally, the limits of integration can be from b to c as long as t_0 is in [b,c]. Otherwise, the integral is zero.

3. Apr 13, 2012

### martnll2

Thanks, I'll try it out after studying for this exam and let you know how it goes :D