Cоnsider аn underwаter аcоustic remоte sensing system for detecting the presence of a mine using signals with frequencies between 5 to 10 kHz. When the reflected signal is received, it is corrupted by snapping shrimp sounds that occur at 24 kHz. We want to design a stable and causal continuous (CT) Butterworth lowpass filter (LPF) to remove the unwanted sounds. The LPF must have 15 kHz cutoff frequency, 24 kHz stopband frequency and at least 30 dB stopband attenuation. (a) 20 pts Find the minimum filter order to meet the specifications of the CT Butterworth LPF and provide all designed LPF parameters; show all steps. (b) 15 pts Use the CT Butterworth LPF design and the bilinear transformation with sampling frequency kHz to design a causal and stable discrete-time (DT) Butterworth LPF. For the design, provide the corresponding DT LPF specifications and the magnitude response of the DT LPF. (c) 15pts Provide the transfer function and pole locations of the DT Butterworth LPF designed in part (b). Determine whether the filter is stable as expected from the design; explain your answer.