H.W. Prove the z-transforms for common sequences summarized in Table 1except the last sequence (15).Table 1Table of z-Transform PairsRegion ofConvergenceLine No.x(n), n 20z-Transform X(2)z(z + 1)(z - 1)°n u(n)z|>16a u(n)z| > la|Z-a7e-na u(n)z|>e-a(z -e-a8na" u(n)azz|> la|(z - a)z sin(a)z2 – 2z cos(a) +19.sin(an)u(n)z|>1zz - cos(a)]z2 - 2z cos(a) + 110cos(an)u(n)z| >1[a sin(b)zz2 - [2a cos(b)]z +a?z[z- a cos(b)]z2 - [2a cos(b)z +a-211a" sin(bn)u(n)z|> la|12a" cos(bn)u(n)z| > la|[e-a sin(b)]zz2 - [2e-a cos(b)]z +e-2a13e-an sin(bn)u(n)z|>e-az[z -ecos(b)Iz2 - (2e-a cos(b)]z +e-2a14e-an cos(bn)u(n)Z|>e-aAzA'Z2|A||P|"cos(n8 + g)u(n)where P and A are complexconstants defined byP = |P|L0, A = |A|L15z-PZ- P

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Answered: z(z + 1) (z – 1)3 n u(n) z|>1 a u(n) z|…

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Electrical Engineering

z(z + 1) (z – 1)3 n u(n) z|>1 a u(n) z| > la| Z-a 7 e-na u(n) z|>e-a (2 - ea) az

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 (15).
Table 1
Table of z-Transform Pairs
Region of
Convergence
Line No.
x(n), n 20
z-Transform X(2)
z(z + 1)
(z - 1)°
n u(n)
z|>1
6
a u(n)
z| > la|
Z-a
7
e-na u(n)
z|>e-a
(z -e-a
8
na" u(n)
az
z|> la|
(z - a)
z sin(a)
z2 – 2z cos(a) +1
9.
sin(an)u(n)
z|>1
zz - cos(a)]
z2 - 2z cos(a) + 1
10
cos(an)u(n)
z| >1
[a sin(b)z
z2 - [2a cos(b)]z +a?
z[z- a cos(b)]
z2 - [2a cos(b)z +a-2
11
a" sin(bn)u(n)
z|> la|
12
a" cos(bn)u(n)
z| > la|
[e-a sin(b)]z
z2 - [2e-a cos(b)]z +e-2a
13
e-an sin(bn)u(n)
z|>e-a
z[z -ecos(b)I
z2 - (2e-a cos(b)]z +e-2a
14
e-an cos(bn)u(n)
Z|>e-a
Az
A'Z
2|A||P|"cos(n8 + g)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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