Therefore 
Ryxx(T1, T2) = 2 | | hp(uj, U2) Rxx(t1 — uy )Rxx(T2 — u2) du;duz (11.46) 
and oo 
2 
1 
Syxx(@1,@2) = | — | | Rexx. t2) exp\—ilo n+ w2t9) dt\dt2 
27 
2 E 
= | | h2(uy, uz) Rxx(t1 — uy) Rxx(t2 — u2) exp[— 1(@1T + W2T2)] 
—co —o~ at dt (11.47) 
SYXx(@1,@2) = 2 H2(@ 1,2) Sxx(@1) - Sxx(@2) (11.48) 
SYXx(@1, @2) 
2sxx(@1) sxx(@2) 
Here with the variables w1,@ 2 into @;’,w2' inverted by 
H>(@ 1, @2) = (11.49) 
1 
@,= 3 1 + @2) 
@1-@2 =] 
Dans aoe (11.50) 
1 , U 
then 
SYXX(@1, @2) = Syxx(@1—@2,W1 + W2) = Syxx(@1,02) J me ay . (11.51) 
2. 
’ 
Since Jacobian 
Le tgaek 
Aste me = = s 5 = > (11.52) 
Py) 
therefore 
Syxx(@1, @2) = Syxx(@1,@2) X : (11.53) 
and 2 syxx(@1—@2,@1 + @2) = Syxx(@1, @2). (11.54) 
Substituting into Eq. 11.49 gives 
Ss @1—@2,0,+@2) 
A2(@1, 2) = Syxx(@1—@2,01+@2) (11.55) 
SxXx(@1) Sxx(2) 
307 
