The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is

The autocorrelation function of an energy signal has

A system having a unit impulse response $$h\left( n \right)$$ = $$u\left( n \right)$$ is excited by a signal $$x\left( n \right)$$ $$ = \,{\alpha ^n}\,\,u\left( n \right).\,$$ Determine the output $$y\left( n \right)$$

In the linear time-invariant system shown in Fig. 1, blocks labeled D represent unit delay elements. Find the expression for $$y\left( n \right),$$ and also the transfer function $${{Y\left( z \right)} \over {X\left( z \right)}}$$ in the $$z$$-domain.