GATE 2024 BM – Question 59

Signals and Systems · LTI Systems and Convolution · 2 marks · Numerical answer

x[n]=u[n]−u[n−5],h[n]=δ[n]−δ[n−1],and y=x*h. Find the sum of y[n] over all integers n, as an integer.

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Correct answer: 0 to 0

Explanation

x is a five-sample rectangular pulse and h is a first difference. Their convolution telescopes to y[n]=x[n]−x[n−1]=δ[n]−δ[n−5]. Summing gives one minus one, zero. Equivalently sum(y)=sum(x)sum(h)=5×0.

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