Continuous Time Signal Laplace Transform · Signals and Systems · GATE EE

The Laplace transform of f(t)=$$2\sqrt{t/\mathrm\pi}$$ is $$s^{-3/2}$$. The Laplace transform of g(t)=$$\sqrt{1/\mathrm{πt}}$$ is

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

The Laplace transformation of f(t) is F(s). Given F(s)=$$\frac\omega{s^2+\omega^2}$$, the final value of f(t) is

Let the Laplace transform of a function f(t) which exists for t > 0 be F₁(s) and the Laplace transform of its delayed version f(1 - $$\tau$$) be F₂(s). Let F₁^*(s) be the complex conjugate of F₁(s) with the Laplace variable set as $$s=\sigma\;+\;j\omega$$. If G(s) =$$\frac{F_2\left(s\right).F_1^\ast\left(s\right)}{\left|F_1\left(s\right)\right|^2}$$ , then the inverse Laplace transform of G(s) is

A function y(t) satisfies the following differential equation:$$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\left(t\right)$$$ where $$\delta\left(t\right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form

The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches

For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$\rightarrow\infty$$ ?

A rectangular current pulse of duration T and magnitude 1 has the Laplace transform

The Laplace transform of $$\left(t^2\;-\;2t\right)u\left(t\;-\;1\right)$$ is