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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

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    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.
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