In the figure is a linear time invariant discrete systme is shown. Blocks labelled $D$ represent unit delay elements. For $n<0$, you may assume that $x$ (n), $y_{1}(n), y_{2}(n)$ are all zero.
- Find the expression for $y_{1}(n)$ and $y_{2}(n)$ in terms of $x(n)$
- Find the transfer function $\frac{Y_{2}(z)}{X(z)}$ in the $z$-domain
- If $\left\{\begin{matrix} x(n) = 1 & ai \; n=0 \\ = 0 & \text{otherwise,} \end{matrix}\right.$ find $y_{2}(n)$