2. (20%, Ch8: IIR Filter Design) Use Python to design a Butterworth digital lowpass filter to satisfy the following specifications: Sep = 0.31, Rp = 0.4dB Sep = 0.51, As = 45dB (a) Use the impulse-invariant method with T = 0.5. (b) Construct the system function in the rational form and plot the log-magnitude response in dB. (c) Plot the impulse function h(n) and the impulse response h,(t) of the analog prototype and compare their shapes. 2. (20%, Ch8: IIR Filter Design) Use Python to design a Butterworth digital lowpass filter to satisfy the following specifications: Sep = 0.31, Rp = 0.4dB Sep = 0.51, As = 45dB (a) Use the impulse-invariant method with T = 0.5. (b) Construct the system function in the rational form and plot the log-magnitude response in dB. (c) Plot the impulse function h(n) and the impulse response h,(t) of the analog prototype and compare their shapes