Q$5$ a$)$ Given a discrete$-$time LTI system characterized by the below transfer function

i$)$ Determine system zeros and poles, and sketch the zero$-$pole plot

ii$)$ How many regions of convergence$($ROCs$)$ could correspond to the transfer function? Comment on system causality and stability for each ROC

iii$)$ Suppose the system is consisting of the series of two LTI system, i$.$e$.$

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$\backslash$mathrm$\{$H$\}(\backslash$mathrm$\{$z$\})=\backslash$mathrm$\{$H$\}1(\backslash$mathrm$\{$z$\})\backslash$mathrm$\{$H$\}2(\backslash$mathrm$\{$z$\})$

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Obtain difference equations for $\backslash (\backslash$mathrm$\{$H$\}1(\backslash$mathrm$\{$z$\})\backslash )$ and $\backslash (\backslash$mathrm$\{$H$\}2(\backslash$mathrm$\{$z$\})\backslash )$ respectively, and draw a block diagram of the system

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$\backslash$mathrm$\{$H$\}(\backslash$mathrm$\{$z$\})$

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