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GATE 2014 EC (EC2) – Question 53

Networks, Signals and Systems · Discrete-time Signals · 2 marks · Numerical answer

$x[n]=n$ for $0\le n\le10$, and zero otherwise. If y[n] is x[n] convolved with itself, find y[4].

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Correct answer: 9.9 to 10.1

Explanation

Discrete convolution gives y[4]=Σkx[k]x[4−k]. Only k=0,1,2,3,4contribute, giving0×4+1×3+2×2+3×1+4×0=**10**. Values of x outside its0through10support are zero.