# Given a signal f (t) = 3t^2+2t+1, which is multiplied by 2 unit delayed version of impulse and integrated over period -∞ to ∞. The resultant is ______________

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Given a signal f (t) = 3t^2+2t+1, which is multiplied by 2 unit delayed version of impulse and integrated over period -∞ to ∞. The resultant is ______________

(a) 1

(b) 6

(c) 17

(d) 16

The question was asked in an interview for job.

I'd like to ask this question from Concept of Convolution in division Signal Transmission Through Linear Systems of Signals and Systems

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The correct choice is (c) 17

The explanation: $\int_{-∞}^∞ f(t) δ(t-t_0) = f (t_0)$

Here, t0 = 2

So, $\int_{-∞}^∞ f(t) δ(t-2)$ = f (2)

Hence, f (2) = 3(2)^2 + 2(2) + 1

= 12 + 4 + 1 = 17.

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