Design a digital Butterworth lowpass filter to have a passband edge frequency of 10 Hz, a stopband edge frequency of 90 Hz, a maximum passband attenuation of 0.5 dB, and a minimum passband attenuation of 20 dB. The sampling frequency is 200 Hz.

Solution:

(i) Compute the normalized digital frequencies:

$ \begin{aligned}\\ &\omega_P=2 \pi \frac{10}{200}=0.314 \mathrm{rad} / \mathrm{s} \quad \text { and } \\\\ &\omega_s=2 \pi \frac{60}{200}=1.8850 \mathrm{rad} / \mathrm{s}\\ \end{aligned}\\ $

Pre-warp the digital frequencies to obtain the frequencies of the analog LPF

$ \begin{aligned}\\ \Omega_P &=\tan (0.314 / 2)=0.1583 \mathrm{rad} / …