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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
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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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
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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