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GATE 2021 EE – Question 41

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

The causal signal with z-transform $z^2(z-a)^{-2}$ is ($u[n]$ is the unit step signal)

  1. $a^{2n}u[n]$
  2. $(n+1)a^nu[n]$
  3. $n^{-1}a^nu[n]$
  4. $n^2a^nu[n]$

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Show answer and explanation

Correct answer: (B) $(n+1)a^nu[n]$

Explanation

$\frac{z^2}{(z-a)^2}=\frac{1}{(1-az^{-1})^2}$, whose causal inverse is $(n+1)a^nu[n]$.