(adsbygoogle = window.adsbygoogle || []).push({}); 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...

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# Homework Help: Convolution Properties and Fourier Transform

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