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The system function of a causal LTI system is 1+z¬! H(2) = (1 – 0.5z-1)(1+ 0.25z-1)' a) What is the region of convergence of H(2)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input ¤(n) that will produce the output %3D d) Find the impulse response h(n) of the system.

The system function of a causal LTI system is 1+z¬! H(2) = (1 – 0.5z-1)(1+ 0.25z-1)' a) What is the region of convergence of H(2)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input ¤(n) that will produce the output %3D d) Find the impulse response h(n) of the system.

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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The system function of a causal LTI system is 1+2-1 H(2) (1 – 0.5z-1)(1+ 0.25z¬1)" a) What is the region of convergence of H(z)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input r(n) that will produce the output y(n) = -G)(-"u(«) – (G(2)"u(-n – 1). d) Find the impulse response h(n) of the system.
Transcribed Image Text:The system function of a causal LTI system is 1+2-1 H(2) (1 – 0.5z-1)(1+ 0.25z¬1)" a) What is the region of convergence of H(z)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input r(n) that will produce the output y(n) = -G)(-"u(«) – (G(2)"u(-n – 1). d) Find the impulse response h(n) of the system.
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