$($a$)$ Develop a suitable block diagram of a maximum likelihood detector. Show that it obeys the following condition to recover the original base band signal.

${\displaystyle \underset{0}{\overset{}{}}}x(t)s_k(t)dt-(\frac{E_k}{2})is$ maximum for $k=1,2,$dotsdotsdots,$M.$

Here $M$ is the number of symbols.