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GATE 2014 EE (EE1) – Question 44

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 2 marks · Multiple choice

$X(z)=1/(1-z^{-3})$ is the Z-transform of a causal sequence x[n]. Find x[2],x[3].

  1. 0 and 0
  2. 0 and 1
  3. 1 and 0
  4. 1 and 1

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Correct answer: (B) 0 and 1

Explanation

Causality selects the right-sided expansion X(z)=1+z⁻³+z⁻⁶+…. Thus x[n]is1at nonnegative multiples of3and0elsewhere. Therefore **x[2]=0,x[3]=1,B**.