The value of R (in ohms) required for maximum power transfer in the network shown in Fig. is

The z-transform of a signal is given by c(z)=$${1 \over 4}{{{z^{ - 1}}(1 - {z^{ - 4}})} \over {{{(1 - {z^{ - 1}})}^2}}}$$. Its final value is

The z-transform F(z) of the function f(nT) = $${a^{nT}}$$ is

$$If\,\,L\left[ {f\left( t \right)} \right]\, = \,F\left( s \right),$$ then $$L\left[ {f\left( {t - T} \right)} \right]$$ is equal to