1. In an impulse invariance design, show that if Hmc(s) is a transfer function of a stable system, the corresponding H(z) is also a transfer function of a stable system.
2. Consider the design of a digital differentiator H(z).
(a) Determine H(z) using the bilinear transform.
(b) Show a realization of this filter.
(c) Find and sketch the magnitude response of this filter, and compare it with that of an ideal differentiator.
(d) If this filter is used primarily for processing audio signals (voice and music) up to 20 kHz, determine a suitable value for T .