The GATE Grind

GATE 2025 IN – Question 39

Signals and Systems · Discrete-time systems and digital filters · 2 marks · Multiple choice

The initially resting causal discrete-time LTI system obeys $y[n]=\frac1\alpha y[n-1]+x[n]$, where $\alpha>1$ is real. If $x[n]=\delta[n-p]$ with $p>10$, the value of $y[p+1]$ is

  1. 0
  2. 1
  3. $1/\alpha$
  4. $1/\alpha^2$

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Show answer and explanation

Correct answer: (C) $1/\alpha$

Explanation

Before the delayed impulse arrives, the initially resting system has zero output.

At n=p, y[p]=1.

At n=p+1 the input is zero, so y[p+1]=(1/α)y[p]=**1/α, C**.