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GATE EC 2015 Official Paper: Shift 2

Option 3 : The entire s - plane

CT 1: Determinants and Matrices

2850

10 Questions
10 Marks
12 Mins

__Analysis__:

ROC defines the region where the Laplace transform exists.

Laplace transform of f(t) is given as:

F(s) = \(\int_{-\infty}^{\infty} f(t) e^{-st} dt=\int_{-\infty}^{\infty} f(t) e^{-\sigma t} e^{-j\omega t} dt\)

It is given that, f(t) < ∞ and the signal is zero outside in the Interval [T1, T2] where T1 & T2 are finite.

If f(t) is multiplied by a decaying Exponential (σ > 0) or by a growing exponential (σ < 0), this Exponential weighting is never unbounded.

Consequently, the Integrability of f(t) by this exponential weighting is not destroyed.

Hence, the ROC of signal f(t) is entire s-plane