GATE 2025 BM – Question 47

Signals and Systems · LTI Systems and Convolution · 2 marks · Multiple select

An LTI system has h[n]=δ[n]+δ[n−1]/2+δ[n−2]/3. Input is x[n]=δ[n]+δ[n−1]. Which output statements hold?

y[2]=11/6
y[2]=5/6
y[k]=0 for all k≥3
y[k]=0 for all k≥4

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Correct answer: (B) y[2]=5/6; (D) y[k]=0 for all k≥4

Explanation

Convolution with two adjacent impulses gives y[n]=h[n]+h[n−1]. Therefore samples n=0,1,2,3 are 1,3/2,5/6,1/3. The n=3 sample is nonzero, but every sample from n=4 onward is zero. Hence B,D.

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