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

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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
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*
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*
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