Consider a first-order LTID system with a pole at z = γ and a zero at z = 1 γ∗ , where |γ| ≤ 1. (a) Show that this system is an allpass filter. That is, show that the magnitude response |H(e jΩ )| is...

Consider a first-order LTID system with a pole at z = γ and a zero at z = 1 γ∗ , where |γ| ≤ 1.

(a) Show that this system is an allpass filter. That is, show that the magnitude

response |H(e^jΩ)| is constant with frequency.

(b) Generalize this result to describe how to construct a Kth-order allpass filter.

May 13, 2022

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