If f1(t) and f2(t) are duration-limited signals such thatf1(t)≠

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If f₁(t) and f₂(t) are duration-limited signals such that
f₁(t) ≠ 0, for 5 < t < 7
= 0, otherwise

f₂(t) ≠ 0, for 1 < t < 3
= 0, otherwise

then the convolution of f₁(t) and f₂(t) is zero every where except for—

1. 1 < t < 7
2. 3 < t < 5
3. 5 < t < 21
4. 6 < t < 10

Correct Option: D

Given

f₁(t)		≠ 0, for 5 < t < 7
		= 0, otherwise

and, f₂(t)		≠ 0, for 1 < t < 3
		= 0, otherwise

Assume that

f(t) = f₁(t)*f₂(t)

=		^∞	f₁(τ ).f₂(t – τ )dτ
		_{– ∞}

Except these two possible range, we get zero output so range, 6 < t < 10.
Hence, alternative (D) is the correct choice.