a(k) = eak coshw.k coshw, k ewok te-wok 2 eak coshw.k eak ewokteake-wok 2 X(Z) 3D글 z(enk e.k) + 글 z(enke-w.k) Z – transform of a" : |Z(a") Z(a") = . - 1 1-az-1 ROC : |Z| > |a| Z-a X(2) = ± ( + Z-eake z-eake-wo because a = e"ew• in Z(ew.k) and a = e"e-w• from equation 1, ed e z-e"e -wo+z-eªewo X(2) = (z-e"e-w) (z-e"ewo) 2z-e“ (e+wo +e¬Wo) X(2) = (z2 –2ea zcoshuwote2a) (z) z²–ze®coshw.K z2–2ze coshw.K+e2a 2/2
a(k) = eak coshw.k coshw, k ewok te-wok 2 eak coshw.k eak ewokteake-wok 2 X(Z) 3D글 z(enk e.k) + 글 z(enke-w.k) Z – transform of a" : |Z(a") Z(a") = . - 1 1-az-1 ROC : |Z| > |a| Z-a X(2) = ± ( + Z-eake z-eake-wo because a = e"ew• in Z(ew.k) and a = e"e-w• from equation 1, ed e z-e"e -wo+z-eªewo X(2) = (z-e"e-w) (z-e"ewo) 2z-e“ (e+wo +e¬Wo) X(2) = (z2 –2ea zcoshuwote2a) (z) z²–ze®coshw.K z2–2ze coshw.K+e2a 2/2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:How did he get the
value inside the line
a (k) = eak coshw,k
-wok
coshw. k
ewok
+e
2
eak ewokteake-wok
eak coshw.k
Z - trans form of a" :
Z(a") =
1
1-az-1
Z(a") =
ROC : |Z| > |a|
Z-a
X(2) = ( +)
....
z-eakewo
z-eake-wo
because a = e“ew• in Z(ew.k) and a = e"e-Wo
from equation 1,
ede-wo
z-e"e-wo +z-e"ewo
|X(2)
(z-e"e-w•)(z-e"ewo)
2z-e" (e+wo+e-wo)
X(2) = -
(z2–2ea zcoshw.te2a)
(z):
z²–ze coshw,K
z2–2ze coshw.K+e2a
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