The GATE Grind

GATE 2014 EC (EC3) – Question 54

Networks, Signals and Systems · LTI Systems · 2 marks · Multiple choice

A causal system has transfer $1/(s+1)$ and impulse response h(t). S1: It is stable. S2: $h(t+1)/h(t)$ is independent of t for t > 0. S3: A noncausal system with the same transfer is stable. Which is true?

  1. Only S1 and S2
  2. Only S2 and S3
  3. Only S1 and S3
  4. All three

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Only S1 and S2

Explanation

The causal realization has h(t)=e⁻ᵗu(t), which is absolutely integrable and stable. For t>0, h(t+1)/h(t)=e⁻¹, independent of t. The noncausal realization is−e⁻ᵗu(−t), which grows toward−∞and is not integrable. Thus **only S1and S2are true,A**.