Prove the z-transforms for common sequences summarized

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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H.W. Prove the z-transforms for common sequences summarized in Table 1
except the last sequence
Table 1 Table of z-Transform Pairs
Region of
Convergence
Line No.
x(n), n20
z-Transform X(z)
z(z+1)
(z – 1)8
n u(n)
zl>1
6
a" u(n)
kl> la|
Z-a
7
e ha u(n)
kl>e
(z -ea)
8
az
na" u(n)
kl> la|
(2- a)?
z sin(a)
z2 – 2z cos(a) +1
z[z – cos(a)]
z2 – 2z cos(a) +1
sin(an)u(n)
kl>1
10
cos(an)u(n)
kl>1
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 Region of Convergence Line No. x(n), n20 z-Transform X(z) z(z+1) (z – 1)8 n u(n) zl>1 6 a" u(n) kl> la| Z-a 7 e ha u(n) kl>e (z -ea) 8 az na" u(n) kl> la| (2- a)? z sin(a) z2 – 2z cos(a) +1 z[z – cos(a)] z2 – 2z cos(a) +1 sin(an)u(n) kl>1 10 cos(an)u(n) kl>1
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