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GATE 2015 EE (EE2) – Question 45

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

For $X(z)=2z+4-4/z+3/z^2$, let y[n] be the first difference x[n]−x[n−1]. Then Y(z) is

  1. $2z+2-8/z+7/z^2-3/z^3$
  2. $-2z+2-6/z+1/z^2-3/z^3$
  3. $-2z-2+8/z-7/z^2+3/z^3$
  4. $4z-2-8/z-1/z^2+3/z^3$

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Correct answer: (A) $2z+2-8/z+7/z^2-3/z^3$

Explanation

A one-sample delay multiplies the bilateral z-transform by z⁻¹. Thus Y(z)=(1−z⁻¹)X(z).

Subtract $2+4/z-4/z^2+3/z^3$ from the given X. Collecting powers gives **2z+2−8/z+7/z²−3/z³, A**.

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