The Z-transform of the following real exponential sequence:
x(nT) = $${a^n}$$, nT $$ \ge $$ 0
=0, nT<0, a> 0
gives us by

The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to a unit step function will be:

The impulse response and the excitation function of a linear time invariant casual system are shown in Fig. a and b respectively. The output of the system at t = 2 sec. is equal to

The magnitude and phase transfer functions for a distortionless filter should respectively be: