Problem $1$: Using prewarping method, consider a lowpass IIR Butterworth filter with the following specifications. $$ Stopband attenuation $>50$ dB $$ Passband edge frequency $2$ kHz $$ Transition band width $0\mathrm{.}5$ kHz $$ Sampling frequency $8$ kHz a$)$ Determine the order of the filter, i$.$e$.,$ N$.$ b$)$ If the order of the filter is greater than $3,$ compute only the first three poles of the continuous Butterworth filter. c$)$ Using only the the poles that you have computed in Part b$,$ write the transfer function equation for the Butterworth filter that has only these poles as its poles. Name it H$($s$).$ d$)$ Using bilinear transformation, find H$($z$)$ from H$($s$)$ that you have computed in Part c$.$