RAr){1 +a;+ aj + a[Rr + 1) + Rr—1)] +.0,0[R fr +1) +Rlr-1)] 
+ a2[R(r+2)+RAr—2)] = Re (r) (5.110’) 
According to the relation between autocovariance and the spectrum, 
=i & jets 
Se + let” = Rr F [jetorF)). pFiw (5.111) 
I Se 
=15(@)) ewe 
Then, transforming both sides of Eq. 5.110’ by Fourier transformation and, taking into 
account Eq. 5.111, 
s(a1 + aj +as+ (a, + ajan\(e™ + &) + ane + | 
1 
= 5<() Seti (5.112) 
1 
sw)|1 + aye + ane? 2 So, (5.112’) 
27 
Thus Sx(@) oe (5.113) 
u = ; : ’ j 
2 r +ajeo@ + ane 2 
from the function a(Z) of Eq. 5.74 
2 
(o} 
sw) = ——————-,, (5.114) 
2| ace) |? 
or 
2 
to} 
$0) = 
2n {a + ajas + 2(a) + a,a7) cos w + 2a) cos 2«)| 
oe 
5 Sg (5.115) 
27 (1 —a2)* + aj + 2a;(1 + a2) cos w + 4a2 cosw) 
Substituting 0? for a2 in Eq. 5.88 gives 
1 —a)[(1 + a2)* —a? Jo? 
S,(w) = CSO aaaaudee (5.115°) 
2m(1 + a){(1 —ay)?* + a;+ 2a;(1 + a2) cosw + 4a2 cos? | 
ds(w) is 
From this expression, and setting 0, 
128 
