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