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GATE EC 2016 Set 1 — Question 40

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MCQ+2 / -0.67MediumLaplace Transform & ROCLTI SystemsSignals & Systems

Signals & Systems → LTI Systems → Laplace Transform & ROC

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Question

The Laplace transform of the causal periodic square wave of period TT shown in the figure below is
A plot of a causal periodic square wave $f(t)$ versus time $t$. The signal has a period $T$. It is equal to 1 for $0 < t < T/2$ and 0 for $T/2 < t < T$. This pattern repeats for $t > 0$.
  1. A.
    F(s)=11+e−sT/2F(s) = \frac{1}{1+e^{-sT/2}}
  2. B.
    F(s)=1s(1+e−sT/2)F(s) = \frac{1}{s(1+e^{-sT/2})}
  3. C.
    F(s)=1s(1−e−sT)F(s) = \frac{1}{s(1-e^{-sT})}
  4. D.
    F(s)=11−e−sTF(s) = \frac{1}{1-e^{-sT}}

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