We wish to design a digital bandpass filter from a second-order analog lowpass Butterworth filter prototype using the bilinear transformation. The specifications on the digital filter are shown in figure. The cutoff frequencies (measured at the half power points) for the digital filter should lie at ? = 5?/12. And w = 7?/12.The analog prototype is given byH(s) = 1/s2 + ?2s + 1with the half-power point at ? = 1.(a) Determine the system function for the digital bandpass filter.(b) Using the same specs on the digital filter as in part (a), determine which of the analog bandpass prototype filters shown in figure could be transformed directly using the bilinear transformation to give the proper digital filter. Only the plot of the magnitude squared of the frequency is given.

IHto2 power points (a) I. 200 II 200 IHIS12 . 300 547 zi(3IHI IV. 600 1019 (b) -Iri