A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrightarrow \limits^{FT} \,{{A{e^{ - j6\pi f}}} \over {1 - \left( {{2 \over 3}} \right){e^{ - j2\pi f}}}}$$ ,
where u(n) donotes the unit step sequence. The values of A is_______________.

The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of g(t) = $$t \cdot f\left( t \right)$$

A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this system casual it needs to be cascaded with another LTI system having a transfer function H₁(s). A correct choice for H₁(s) among the following options is

A casual LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related through the linear constant - coefficient differential equation $$${{{d^2}y\left( t \right)} \over {d{t^2}}} + \alpha {{dy\left( t \right)} \over {dt}} + {\alpha ^2}y\left( t \right) = x\left( t \right).$$$

Let another signal g(t) be defined as $$\left( t \right) = {\alpha ^2}\int_0^t {h\left( \tau \right)d\tau + {{dh\left( t \right)} \over {dt}} + \alpha h\left( t \right)} $$.

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is ______.