GATE EE 2025 Set 1 — Question 20
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Signals & Systems → LTI Systems → Convolution Integral & Sum
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Question
Consider a discrete-time linear time-invariant (LTI) system , whereLetwhere is the discrete-time unit impulse function. For an input signal , the output is
Correct answer
(A) x[n] + x[n - 1] + x[n - 2]
Solution
The impulse response of the system is defined as the output when the input is a unit impulse .
Given:
This can be written as: For any LTI system, the output for an input is given by the convolution sum:
Using the property :
Given:
This can be written as: For any LTI system, the output for an input is given by the convolution sum:
Using the property :
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