If L$$\left[ {f\left( t \right)} \right]$$ = $$\omega /\left( {{s^2} + {\omega ^2}} \right),$$ then the value of $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr } $$

The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is

The transfer function of a zero - order - hold system is

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e^-at u(t), a>0 will be