The GATE Grind

GATE 2017 EC – Question 16

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

Consider a single input single output discrete-time system with $x[n]$ as input and $y[n]$ as output, where the two are related as

$$y[n] = \begin{cases} n|x[n]|, & \text{for } 0 \leq n \leq 10 \\ x[n] - x[n-1], & \text{otherwise.} \end{cases}$$

Which one of the following statements is true about the system?

  1. It is causal and stable
  2. It is causal but not stable
  3. It is not causal but stable
  4. It is neither causal nor stable

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Show answer and explanation

Correct answer: (A) It is causal and stable

Explanation

Each output depends only on the present and past inputs, so the system is causal. For $0 \leq n \leq 10$ the output is bounded by $10 \times$ the input bound, and elsewhere it is bounded by twice the input bound. So a bounded input gives a bounded output, and the system is stable.