H.W. Prove the z-transforms for common sequences summarized in Table 1except the last sequenceTable 1 Table of z-Transform PairsLine No.Region ofConvergencex(n), n20z-Transform X(z)[a sin(b)]z22 - [2a cos(b)l +a?11a' sin(bn)u(n)z|> la|zlz -a cos(b)|2 - [2a cos(b)z +a 212a" cos(bn)u(n)kl> la|fe sin(b)zz2- [2e "cos(b)]z +e2z -e cos(b)]z2 – [2e-a cos(b)]z +e-2a13e an sin(ta)u(n)kl>ea2a14e an cos(b:}u(n)kl>e aAzA*Z2|A||P|"cos(n0 +9)u(n)where P and A are complexconstants defined byP = |P|L0, A = A|L15Z-PZ- P*

Answered: Image /qna-images/answer/c5dba9e6-dee1-4f84-af9a-992130f19779.jpg

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...

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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*

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