The GATE Grind

GATE 2024 IN – Question 13

Signals and Systems · Signals and linear time-invariant systems · 1 mark · Multiple choice

A discrete-time sequence is $x[n]=[1,2,3,4]$ for $0\le n\le3$. Its zero-lag autocorrelation is

  1. 1
  2. 10
  3. 20
  4. 30

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Correct answer: (D) 30

Explanation

Unnormalised zero-lag autocorrelation is the sequence energy: $R_{xx}[0]=\sum_n|x[n]|^2=1+4+9+16=30$. No normalisation by sequence length is specified.

Answer: **D**.