GATE EE 2023 Set 1 — Question 31
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Signals & Systems → LTI Systems → Convolution Integral & Sum
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Question
For the signals and shown in the figure, is maximum at . Then in seconds is ___________ (Round off to the nearest integer).
Correct answer
4 to 4
Solution
The convolution is defined as . Given that is a rectangular pulse of width 2 centered at ( for ), the integral simplifies to . By substituting , we obtain . This integral represents the area under the signal within a sliding window of width 2. From the provided graph of , the signal is a ramp that increases linearly from to . For an increasing function, the area under a window of fixed width is maximized when the window is positioned at the furthest possible point to the right. Therefore, the window should end at , which implies , or . Thus, .
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