$($a$)$ A digital filter design for a specific application has the following impulse response:

$\backslash [$

y$($n$)=$a x$($n$)+$b x$($n$-2)+$c x$($n$-3)$

$\backslash ]$

i$)$ Explain, with the help of diagrams, a simple and pipelined implementation of the filter.

ii$)$ Determine the maximum operating frequency of the simple and pipelined models. Given: An adder incurs $10$ ps of delay and a multipler incurs $25$ ps of delay.

iii$)$ Determine the latency and throughput of the simple and pipelined models, assuming the same delays as above. Comment on the latency and throughput results.

iv$)$ Provide an expression for output $\backslash ($ y$\_\{$p p$\}\backslash )$ the output of the pipelined system.