GATE 2023 BM – Question 47
Sequences x₁[n] and x₂[n] have samples [1,2,1] and [1,1,2] respectively for n=0,1,2 and are zero elsewhere. Let x=x₁*x₂. Which statements are correct?
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Correct answer: (A) x[2]=x[3]; (D) x[2]=5
Explanation
Direct convolution gives x[0]=1; x[1]=1+2=3; x[2]=2+2+1=5; x[3]=4+1=5; x[4]=2. Hence x[2]=x[3] and x[2]=5, so A and D. The other proposed numerical samples are incorrect.