GATE EC 2022 Set 1 — Question 33
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Signals & Systems → Continuous-Time Signals → Impulse Response & Convolution
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Question
Let and , where denotes the unit step function. If denotes the convolution of and , then \lim_{t \to \infty} y(t) = \text{_________}
(rounded off to one decimal place).
(rounded off to one decimal place).
Correct answer
0 to 0
Solution
Given the signals:
The convolution can be analyzed using the Laplace Transform:
The Laplace transform of the output is:
To find the steady-state value , we apply the Final Value Theorem:
Evaluating the limit at :
Alternatively, by direct integration for :
As , the term , hence .
The convolution can be analyzed using the Laplace Transform:
The Laplace transform of the output is:
To find the steady-state value , we apply the Final Value Theorem:
Evaluating the limit at :
Alternatively, by direct integration for :
As , the term , hence .
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