H.W. Prove the z-transforms for common sequences summarized in Table except the last sequence Table 1 Table of z-Transform Pairs Line No. Region of Convergence x(n), n20 z-Transform X(z) [a sin(b)z 22 - [2a cos(b)z+a? zz -a cos(b)| 2 - 2a cos(l)z +a 2 11 a sin(bn)u(n) kl> lal 12 a cos(bn)u(n) kl> la| fea sin(b)]z z2 - |2e "cos(b)z +e 13 e an sin(ta)u(n) kl>ea 2a zk -ecos(b)] 2 - [2ea cos(b)z+e-2a 14 an cos(bu{n} kl>e a e
H.W. Prove the z-transforms for common sequences summarized in Table except the last sequence Table 1 Table of z-Transform Pairs Line No. Region of Convergence x(n), n20 z-Transform X(z) [a sin(b)z 22 - [2a cos(b)z+a? zz -a cos(b)| 2 - 2a cos(l)z +a 2 11 a sin(bn)u(n) kl> lal 12 a cos(bn)u(n) kl> la| fea sin(b)]z z2 - |2e "cos(b)z +e 13 e an sin(ta)u(n) kl>ea 2a zk -ecos(b)] 2 - [2ea cos(b)z+e-2a 14 an cos(bu{n} kl>e a e
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...
Related questions
Question
![H.W. Prove the z-transforms for common sequences summarized in Table 1
except the last sequence
Table 1 Table of z-Transform Pairs
Line No.
Region of
Convergence
x(n), n20
z-Transform X(z)
[a sin(b)]z
22 - [2a cos(b)l +a?
11
a' sin(bn)u(n)
z|> la|
zlz -a cos(b)|
2 - [2a cos(b)z +a 2
12
a" cos(bn)u(n)
kl> la|
fe sin(b)z
z2- [2e "cos(b)]z +e
2z -e cos(b)]
z2 – [2e-a cos(b)]z +e-2a
13
e an sin(ta)u(n)
kl>ea
2a
14
e an cos(b:}u(n)
kl>e a
Az
A*Z
2|A||P|"cos(n0 +9)u(n)
where P and A are complex
constants defined by
P = |P|L0, A = A|L
15
Z-P
Z- P*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00d501a7-d83a-4ad4-9904-4d3237384911%2Fc5dba9e6-dee1-4f84-af9a-992130f19779%2Fp3gu8yt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:H.W. Prove the z-transforms for common sequences summarized in Table 1
except the last sequence
Table 1 Table of z-Transform Pairs
Line No.
Region of
Convergence
x(n), n20
z-Transform X(z)
[a sin(b)]z
22 - [2a cos(b)l +a?
11
a' sin(bn)u(n)
z|> la|
zlz -a cos(b)|
2 - [2a cos(b)z +a 2
12
a" cos(bn)u(n)
kl> la|
fe sin(b)z
z2- [2e "cos(b)]z +e
2z -e cos(b)]
z2 – [2e-a cos(b)]z +e-2a
13
e an sin(ta)u(n)
kl>ea
2a
14
e an cos(b:}u(n)
kl>e a
Az
A*Z
2|A||P|"cos(n0 +9)u(n)
where P and A are complex
constants defined by
P = |P|L0, A = A|L
15
Z-P
Z- P*
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 7 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
![Introductory Circuit Analysis (13th Edition)](https://www.bartleby.com/isbn_cover_images/9780133923605/9780133923605_smallCoverImage.gif)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
![Delmar's Standard Textbook Of Electricity](https://www.bartleby.com/isbn_cover_images/9781337900348/9781337900348_smallCoverImage.jpg)
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
![Fundamentals of Electric Circuits](https://www.bartleby.com/isbn_cover_images/9780078028229/9780078028229_smallCoverImage.gif)
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
![Electric Circuits. (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780134746968/9780134746968_smallCoverImage.gif)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
![Engineering Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780078028151/9780078028151_smallCoverImage.gif)
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,