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GATE 2026 EC – Question 16

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

The response of a discrete time system $y[n]$ obeys the following relation: $y[n]=\frac56 y[n-1]-\frac16 y[n-2]+x[n]$. The input to the system is $x[n]=\delta[n]-\frac13\delta[n-1]$. Which of the following options is TRUE for $y[n]$?

  1. Stable and causal response
  2. Stable and non-causal response
  3. Unstable and causal response
  4. Unstable and non-causal response

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Show answer and explanation

Correct answer: (A) Stable and causal response

Explanation

$H(z)=1/[(1-\tfrac12z^{-1})(1-\tfrac13z^{-1})]$ and $X(z)=1-\tfrac13z^{-1}$. So $Y(z)=1/(1-\tfrac12z^{-1})$, giving $y[n]=(1/2)^nu[n]$, which is stable and causal.