z2-ze coshw.K (z) z2– 2ze coshw.K+e2a -
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
x(k) = eak coshw,k
-wok
coshw. k
ewok
+e
2
eak coshw, k
eak
ewokteake-wok
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)
= 5
(z-e"e-w)(z-e"ewo)
22-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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