2 2) 
Oi Oo (6.72) 
0) : 
©) DAA, + A2) 4kw? 
The autocovariance coefficient 0(s) is 
Ages — Aye 
= 6.72’ 
COs cae (6.72) 
If this is a real process, then R(—s) = R(s) and 
5 isl Isl 5 
R(S\ = peu eae 2s) 6.71 
(s) Dalg(A2 aad | 2 1 ) ( ) 
Therefore, from the Fourier transform, the spectrum is, after manipulation, 
s(0) == | R(s)e5ds 
oF { Azet!s! 1 e42!s!y 
Qn 2 yA2(A2 —23) 
—-co 
e Sds 
0% 1 
2 
2x \iw? +a1(iw) +a 
eC ieee ee SS (6.73) 
2n (w*—w2) + 4k*w rw? 
If we use Eq. 6.54, 
(D? + Day + ao)X(t) = Z(t) 
a(D)X(t) = Z(t). 
Here a(Z) = Z*+a,D +o. 
Then from Eq. 6.73 
oO 1 ; 
(Oo (6.73’) 
This form is similar to Eq. 5.114, which is the expression for the discrete process 
AR(2). 
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