1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Convolution Homework Involving Impulse Functions

  1. Apr 13, 2012 #1
    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. jcsd
  3. Apr 13, 2012 #2
    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.
    [tex]\int\limits_{-\infty}^{\infty} \delta(t-t_0)a(t)dt=a(t_0)[/tex]
    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.
  4. Apr 13, 2012 #3
    Thanks, I'll try it out after studying for this exam and let you know how it goes :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook