A second-order analog Butterworth filter has a transfer function

(a) Is the half-power frequency of this filter Ω_­hp = 1 rad/sec?

(b) To obtain a discrete Butterworth filter we choose the bilinear transformation

What is the half-power frequency of the discrete filter?

(c) Find the transfer function H(z) when we use the above bilinear  transformation.

(d) Plot the poles and zeros of H(s) and H(z). Are both of these filters  BIBO stable?

H(s : s2 + V2s + 1 -1 s = K- ,K = 1 -1' 1+z