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Suppose we know the system function H(z) of a discrete-time LTI system has a pair , double poles at p3 = P4 = -2, of complex-conjugate poles at pi 0.4e¹ and p2 0.4e = two zeros at z1 = 1,22 = − 1, and double zeros at the origin z3 = z4 = 0. (a) What is the expression for H(z)? (b) Suppose h(n) = Z-¹ [H(2)] is a causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable? = (c) Suppose h(n) = Z-¹[H(z)] is an anti-causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable?

Suppose we know the system function H(z) of a discrete-time LTI system has a pair , double poles at p3 = P4 = -2, of complex-conjugate poles at pi 0.4e¹ and p2 0.4e = two zeros at z1 = 1,22 = − 1, and double zeros at the origin z3 = z4 = 0. (a) What is the expression for H(z)? (b) Suppose h(n) = Z-¹ [H(2)] is a causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable? = (c) Suppose h(n) = Z-¹[H(z)] is an anti-causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable?

Introductory Circuit Analysis (13th Edition)
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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Suppose we know the system function H(z) of a discrete-time LTI system has a pair of complex-conjugate poles at p₁ = = 0.4e¹ and p2 = 0.4e-15, double poles at p3 = P4 = −2, two zeros at 2₁ = 1,22 = -1, and double zeros at the origin z3 = 24 = 0. (a) What is the expression for H(z)? (b) Suppose h(n) = Z−¹[H(z)] is a causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable? (c) Suppose h(n) = Z−¹[H(z)] is an anti-causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable?
Transcribed Image Text:Suppose we know the system function H(z) of a discrete-time LTI system has a pair of complex-conjugate poles at p₁ = = 0.4e¹ and p2 = 0.4e-15, double poles at p3 = P4 = −2, two zeros at 2₁ = 1,22 = -1, and double zeros at the origin z3 = 24 = 0. (a) What is the expression for H(z)? (b) Suppose h(n) = Z−¹[H(z)] is a causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable? (c) Suppose h(n) = Z−¹[H(z)] is an anti-causal system. What is ROC of H(z)? Determine h(n). Is the system BIBO stable?
(d) Suppose h(n) = Z−¹[H(z)] is a BIBO stable system. What is ROC of H(z)? Determine h(n). Hint: You can determine h(n) up to a constant.
Transcribed Image Text:(d) Suppose h(n) = Z−¹[H(z)] is a BIBO stable system. What is ROC of H(z)? Determine h(n). Hint: You can determine h(n) up to a constant.
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