The GATE Grind

GATE 2014 EC (EC3) – Question 55

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

$X(z)=1/(1-2z^{-1})^2$, ROC |z| > 2. Find x[2].

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 11.9 to 12.1

Explanation

For |z|>2, expand(1−2z⁻¹)⁻²=Σₙ₌₀∞(n+1)2ⁿz⁻ⁿ. Hence x[n]=(n+1)2ⁿu[n] and **x[2]=3×4=12**. The ROC establishes the right-sided sequence; the same algebraic transform with another ROC would mean something different.