Suppose you have a transfer function given by

H$($s$)=($s$)/($s$^(2)+\backslash$sqrt$(2)$s$+1)$

which is a classic prototype Butterworth bandpass filter with a normalized center frequency of $1$

ra$($d$)/($sec$).$

$($a$)$ Use this prototype to design an IIR filter that will have a center frequency of $7$ kHz for a signal

sampled at F$\_($s$)=40,000$Hz

$($b$)$ For that design, where on the DT frequency axis does the center frequency end up$?$