$(2)$ A second order IIR filter has the following transfer function parameters:

Poles are given by: p$\_(1,2)=(0\mathrm{.}9)/(+)-60\backslash$deg $.$

Zeros are given by: z$\_(1,2)=(1)/(\_(+))-60\backslash$deg $.$

A sampling frequency f$\_($samp$)=2$kHz$.$

A DC magnitude response equivalent to $20$ dB $.$

$($a$)$ Construct the transfer function of the filter, namely H$($z$).$

$^(1)$ please turn the page over

$($b$)$ Determine the frequency response of the filter H$($e$^($j$\backslash$omega $)).$ Hence, plot the magnitude response.

What kind of filter is it$?$

$($c$)$ Determine the frequencies in Hz $,$ at which the magnitude responses are $1$ and $0.$

$($d$)$ Write out the difference equation of the filter. Hence, draw the block diagram of the diff.

equation, then calculate the min. number of multiplications $()/($sec$).$

$($e$)$ Derive an expression for the step$-$response of the filter. Hence, determine and plot the

steady$-$state and transient responses.

$($f$)$ Calculate the transient duration in msec.