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GATE 2014 EC (EC4) – Question 53

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

A stable LTI system has $H(s)=1/(s^2+s-6)$. To make the cascade causal, select a transfer H₁(s) to cascade with it.

  1. $s+3$
  2. $s-2$
  3. $s-6$
  4. $s+1$

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Show answer and explanation

Correct answer: (B) $s-2$

Explanation

Factor H(s)=1/[(s+3)(s−2)]. Stability requires its ROC−3<Re(s)<2, making the s=2component left-sided. Multiplying by **H1(s)=s−2,B** cancels that pole, leaving1/(s+3)with the stable right-sided realization e⁻³ᵗu(t). The cascade factor is an ideal differentiating operator, interpreted distributionally.