1. Find the transfer function H(s) and plot the magnitude response for a bandstop Butterworth filter that satisfies α p ≤ 3 dB, α s ≥ 24 dB, ω p1 ≥ 20 rad/s, ω p2 ≤ 60 rad/s, ω s1 ≤ 30 rad/s, and ω s2...

1.
Find the transfer function H(s) and plot the magnitude response for a bandstop Butterworth filter that satisfies α_p
≤ 3 dB, α_s
≥ 24 dB, ω_p1
≥ 20 rad/s, ω_p2
≤ 60 rad/s, ω_s1
≤ 30 rad/s, and ω_s2
≥ 38 rad/s.

2. Show that CK satisfies the recursion CK(x)=2xC_K−1(x)−C_K−2(x) for K > 1. To do so, expand Eq. (2.42) using Euler’s equation, substitute the result into the right-hand side of the recursion relation, and then simplify