GATE EE 2025 Set 1 — Question 21
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Signals & Systems → Signal Representation → Impulse, Step & Ramp
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Question
Consider a continuous-time signalwhere is the continuous-time unit step function. Let be the continuous-time unit impulse function. The value ofis
Correct answer
(A) -9
Solution
The sifting property of the unit impulse function states that:In this problem, we have , which means .
So, the integral is equal to .Given :
Since for and for :
Therefore:
So, the integral is equal to .Given :
Since for and for :
Therefore:
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