Question $1(40$ points$)$: DSP Filter Block Diagram

The following block diagram shows a cascaded digital signal processing filter block.,

x

$($a$)(7$ Pts$.)$ Determine the system by the operator equations.

$($b$)(8$ Pts$.)$ Determine the difference equation, which should read $\backslash (\backslash$mathrm$\{$y$\}[\backslash$mathrm$\{$n$\}]=\backslash )\backslash (\backslash$qquad $\backslash )$

$($c$)(15$ Pts$.)$ Find the poles by using Python. Does the system converge to zero?

$($d$)(10$ Pts$.)$ By using the operator's equation, perform partial fraction expansion on the polynomial so that the operator equation is a sum of first ordered systems. Use Python for the solution. From this, determine an equivalent block diagram model.