In Fig. 1, a linear time invariant discrete system is shown. Blocks labeled D represent unit delay elements. For $$n\, < 0,$$ you may assume that $$x\left( n \right),$$ $${y_1}\left( n \right),\,\,{y_2}\left( n \right)$$ are all zero.

(a) Find the expression for $${y_1}\left( n \right)$$ and $${y_2}\left( n \right)$$ in terms of $$x\left( n \right).$$
(b) Find the transfer function $${y_2}\left( z \right)/X\left( z \right)$$ in the $$z$$-domain.
(c) If $$x\left( n \right) = 1$$ at $$n = 0$$ or $$x\left( n \right) = 0$$ otherwise

Find $${y_2}\left( n \right).$$