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GATE EC 2014 Set 4 — Question 54

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NAT+2 / -0HardDifferential & Difference EquationsLTI SystemsSignals & SystemsLaplace Transform & ROCPoles & Zeros

Signals & Systems → LTI Systems → Differential & Difference Equations

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Question

A causal LTI system has zero initial conditions and impulse response h(t)h(t). Its input x(t)x(t) and output y(t)y(t) are related through the linear constant-coefficient differential equationd2y(t)dt2+αdy(t)dt+α2y(t)=x(t).\frac{d^2y(t)}{dt^2} + \alpha \frac{dy(t)}{dt} + \alpha^2 y(t) = x(t).Let another signal g(t)g(t) be defined asg(t)=α2∫0th(τ)dτ+dh(t)dt+αh(t).g(t) = \alpha^2 \int_0^t h(\tau) d\tau + \frac{dh(t)}{dt} + \alpha h(t).If G(s)G(s) is the Laplace transform of g(t)g(t), then the number of poles of G(s)G(s) is _____.
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