E[X, - X17) + a7E[X 1 - X71] + @SE[X 2 X12] 
+ ayE[X, - X;,-1] + @102E[X;_1X 1-7-2] + @2[X, - X12] 
+ ay E[X,_, X;_1] + 02E[X,,-1 - X;_-2] + @2E[X_, - X12] 
= Ele, € nr) + b7E [E11 > €rr1) + DE [E11 - €1] 
+ bi Ele; - €,+], 
Ryu) +a+ a3| + ay[R,(r + 1) + Re(r—1)] + aya9[Ry(r + 1) + Rr — 1) 
+ a2[R(r+ 2) + R,(r—2)] 
= Re(r) {1 +3] + bilRe( +1) + Re(r—1)]. (5.179) 
Here we use the relation shown by Eq. 5.111 
a > Rr elena OS Re = Wears Vere 
21 I 2m I 
= s(w)-e* ©. 
Taking the Fourier transform of both sides of Eq. 5.179 gives 
s{o){1 + at + as +(a,+a\a yer” + el”) + ar(e2 + erin} 
= Se (W){1 + b2+ by (ei? + 2%] 
1 ! 
== o2(1 +b} + bye +e), (5.180) 
1 
(«| +ajeo" +a ey 2= 5o0e [1 + bye 2 (5.181) 
2) —iw | 2 
o¢ Ble 
Therefore SAW) = cance (5.182) 
2n lace”) 
r +b,e@ | 2 
2 
(o} 
— SSS (5.182’) 
2m rl +a, eo” + ane] 2 
2 {1 +b?+ 2b (ec + e'”y| 
21 {1 + a?+ a3+ (a, +41a2)(e + e&) + an(e™ + erin} 
LG 1+b?+2b,cosw 
2a [1+a?+a4+ 2a\(1+a)cosw +2az cos2w ] (5.182”) 
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