Suppose we know the system function H(z) of a discrete-time LTI system has a pairof 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). Isthe system BIBO stable?(c) Suppose h(n) = Z−¹[H(z)] is an anti-causal system. What is ROC of H(z)? Determineh(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)? Determineh(n).Hint: You can determine h(n) up to a constant.

d) need to find stable response h(n)= Z-1(H(Z)) For causal system, the ROC is outer side of outermost pole. For anti causal system, the ROC is inner side of the innermost pole. For stable systems, the ROC includes unit circle. i.e |Z| = 1.

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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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Rectangular Coordinate System

In a rectangular coordinate system, each point based on the pair of coordinates is specified uniquely in the plane. From two fixed perpendicular lines, these coordinates are at a distance in the rectangular coordinate system. Each line is known as the reference axis and axes as plural. The point where they meet is called the origin (0,0).

Question

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.

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