4. Consider designing a digital filter with transfer function H(z) from an analog filter with transfer function H.(s) using the following s-to-z mapping: H(z) = H.(s)|=(1-z“ya+z*»] %3D where a is a nonzero integer and B is real. a) If a > 2, for what values of B does a stable, causal analog H.(s) lead to a stable, causal digital filter H(z)? Please mathematically justify your answer. b) If a < -1, for what values of B does a stable, causal analog filter H(s) lead to a stable, causal digital filter H(z)? Please mathematically justify your answer. c) For a = 2 and ß = 2, determine the relationship between the frequency variables in the analog and digital domains, N and w.

4. Consider designing a digital filter with transfer function H(z) from an analog filter with transfer function H.(s) using the following s-to-z mapping: H(z) = H.(s)|=(1-z“ya+z*»] %3D where a is a nonzero integer and B is real. a) If a > 2, for what values of B does a stable, causal analog H.(s) lead to a stable, causal digital filter H(z)? Please mathematically justify your answer. b) If a < -1, for what values of B does a stable, causal analog filter H(s) lead to a stable, causal digital filter H(z)? Please mathematically justify your answer. c) For a = 2 and ß = 2, determine the relationship between the frequency variables in the analog and digital domains, N and w.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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