A source of angular frequency 1rad/sec has source impedance consisting of $$1\Omega$$ resistance in series with 1H inductance. The load that will obtain maximum power transfer is

A sequence $$x\left( n \right)$$ with the $$z$$-transform $$X\left( z \right)$$ $$ = {z^4} + {z^2} - 2z + 2 - 3{z^{ - 4}}$$ is applied as an input to a linear, time-invariant system with the impulse response $$h\left( n \right) = 2\delta \left( {n - 3} \right)$$
where $$\matrix{ {\delta \left( n \right) = 1,} & {n = 0} \cr {0,} & {otherwise} \cr } $$

The output at $$n = 4$$ is

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be