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For causal LTI systems with transfer func- tions listed below, find the zeros and poles and state whether or not each system is stable with a brief jus- tification for why. If the system is stable, find the impulse response for the system. a.) b.) Ĥa(z) Ĥ₁(z) = 222 +5.52 +3.75 22 +0.35z 1.125 - 222 +2.52 +3.75 z2 +0.35z 1.125

For causal LTI systems with transfer func- tions listed below, find the zeros and poles and state whether or not each system is stable with a brief jus- tification for why. If the system is stable, find the impulse response for the system. a.) b.) Ĥa(z) Ĥ₁(z) = 222 +5.52 +3.75 22 +0.35z 1.125 - 222 +2.52 +3.75 z2 +0.35z 1.125

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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For causal LTI systems with transfer functions listed below, find the zeros and poles and state whether or not each system is stable with a brief justification for why. If the system is stable, find the impulse response for the system. a.) \[ \hat{H}_a(z) = \frac{2z^2 + 5.5z + 3.75}{z^2 + 0.35z - 1.125} \] b.) \[ \hat{H}_b(z) = \frac{2z^2 + 2.5z + 3.75}{z^2 + 0.35z - 1.125} \]
Transcribed Image Text:For causal LTI systems with transfer functions listed below, find the zeros and poles and state whether or not each system is stable with a brief justification for why. If the system is stable, find the impulse response for the system. a.) \[ \hat{H}_a(z) = \frac{2z^2 + 5.5z + 3.75}{z^2 + 0.35z - 1.125} \] b.) \[ \hat{H}_b(z) = \frac{2z^2 + 2.5z + 3.75}{z^2 + 0.35z - 1.125} \]
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