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