Q$2$:

$($a$)$ Show that the discrete system described by the System Function H$($z$)$ is non$-$causal.

$H(z)=\frac{1-z^{-1}-0\mathrm{.}25z^{-2}+0\mathrm{.}25z^{-3}}{0\mathrm{.}81z^{-3}+z^{-1}}$

$($b$)$ Using $H(z)$ design a new causal discrete system that will have the same magnitude frequency response as $H(z).$ Using discrete frequencies $=\frac{}{2}$ and $=$ confirm your design.

$($c$)$ Derive the impulse resiponses of the two systems of part $($a$)$ and $($b$)$ above and make a sketch of these.

$($d$)$ Construct a direct realisation and a canonical realisation of the causal system designed in part $($b$)$ above. $[$This will be covered in the Digital Filters section of the class$]$