We wish to design a digital bandpass filter from a second-order analog lowpass Butterwor...

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 Fig. P10.23(a). The cutoff frequencies (measured at the half-power points) for the digital filter should lie at

The analog prototype is given by

with the half-power point at

(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 Fig. P10.23(b) 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.