The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$$p(t) = {{\sin \,4\,\pi \,W\,t} \over \matrix{ 4\,\pi \,W\,t(1 - 16{W^2}{t^2}) \hfill \cr \hfill \cr \hfill \cr} }$$$ The value of p(t) at $$t = {1 \over {4\,W}}$$ is

In delta modulation, the slope overload distortion can be reduced by

A Hilbert transformer is a

The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is