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 Properties and Fourier Transform

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine whether the assertions are true or false, explain.
    (a) If (f * g)(t) = f(t), then g(t) must be an impulse, d(t).
    (b) If the convolution of two functions f1(t) and f2(t) is identically zero,
    (f1 * f2)(t) = 0
    then either f1(t) or f2(t) is identically zero, or both are identically zero.

    2. Relevant equations

    Fourier Transform implies that Xf1(jw)*Xf2(jw)=transform on the convolution.

    3. The attempt at a solution
    a) If Xf1(jw)*Xf2(jw)=Xf1(jw) then Xf2(jw) must be equal to 1, which is the same as d(t).

    Not sure about b...
  2. jcsd
  3. Nov 5, 2011 #2

    I like Serena

    User Avatar
    Homework Helper

    Welcome to PF, Pewgs! :smile:

    Your (a) looks good!

    For (b) you should perhaps consider 2 transforms that multiply to zero, but are not zero themselves.
    For instance a Heaviside function and its mirror.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook