Design an IIR low pass filter $($from scratch$)$ using Butterworth filter model to have a

frequency response as flat as possible in the passband. Consider T $=1.$

Filter Specification: Passband: $0\mathrm{.}92|()|21\mathrm{.}000\mathrm{.}2$

Stopband: $|()|20\mathrm{.}010\mathrm{.}4$

a$)$ Determine the order, the poles, and the transfer function for this filter in the analog domain. b$)$ Utilize the bilinear transformation to obtain a digital low pass filter. Consider T $=1.$ c$)$ Discuss the filter stability in both analog and digital domains.