Question $2.$ For each following difference equations

I. ypkq $0\mathrm{.}2$ypk $1$q $`$ upkq

II$.$ ypk $`1$q $0\mathrm{.}1$ypkq $`0\mathrm{.}2$upkq, yp$0$q $0$

III. ypkq $0\mathrm{.}7$ypk $1$q $`0\mathrm{.}1$ypk $2$q $0\mathrm{.}5$upkq $$ upk $2$q

a$)$ Find the transfer function $($with u being the input and y being the output$)$

b$)$ Compute the final value of the output $($limk$`8$ ypkq$)$ for a sampled step input

c$)$ Compute the $8$ first output samples for a sampled unit step input $($start from k $0)$

d$)$ Draw the temporal evolution of the output for a sampled step input