Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Determine A(z), ROC. What is the relationship between p and q to produce a valid ROC? p", 1, g", n > 0 а(п) - n = 0 n < 0

Determine A(z), ROC. What is the relationship between p and q to produce a valid ROC? p", 1, g", n > 0 а(п) - n = 0 n < 0

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...
See similar textbooks
icon
Related questions
Question

Find Z-transforms and corresponding regions of convergence for

**Title: Analyzing the Z-Transform and Region of Convergence (ROC) for a Given Sequence** **Objective:** Determine the Z-transform \( A(z) \) and the Region of Convergence (ROC). Analyze the relationship between parameters \( p \) and \( q \) necessary to produce a valid ROC. **Given Sequence:** \[ a(n) = \begin{cases} p^n, & n > 0 \\ 1, & n = 0 \\ q^n, & n < 0 \end{cases} \] **Explanation:** - For \( n > 0 \), the sequence is \( p^n \). - For \( n = 0 \), the sequence value is \( 1 \). - For \( n < 0 \), the sequence is \( q^n \). **Task:** To determine the valid ROC, examine the conditions under which the Z-transform converges. The behavior of the sequence for \( n > 0 \) and \( n < 0 \) contributes to different half-planes of convergence in the Z-domain. It is necessary to establish conditions on \( p \) and \( q \) so that these half-planes result in a region of intersection—an essential criterion for a valid ROC.
Transcribed Image Text:**Title: Analyzing the Z-Transform and Region of Convergence (ROC) for a Given Sequence** **Objective:** Determine the Z-transform \( A(z) \) and the Region of Convergence (ROC). Analyze the relationship between parameters \( p \) and \( q \) necessary to produce a valid ROC. **Given Sequence:** \[ a(n) = \begin{cases} p^n, & n > 0 \\ 1, & n = 0 \\ q^n, & n < 0 \end{cases} \] **Explanation:** - For \( n > 0 \), the sequence is \( p^n \). - For \( n = 0 \), the sequence value is \( 1 \). - For \( n < 0 \), the sequence is \( q^n \). **Task:** To determine the valid ROC, examine the conditions under which the Z-transform converges. The behavior of the sequence for \( n > 0 \) and \( n < 0 \) contributes to different half-planes of convergence in the Z-domain. It is necessary to establish conditions on \( p \) and \( q \) so that these half-planes result in a region of intersection—an essential criterion for a valid ROC.
Expert Solution
Step 1

Electrical Engineering homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS