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