From Eq. 11.11, and as E[X(t-7)] = 0, 
8 
my = E[Y(t)] = | ho(t1,T2) E[X(t—11) -X(t—T2)] at - dt2 
= | | h2(t1,T2) Rxx(t2—71) at\dt2 (11.33) 
Sxx(@) exp iw(T2 —T) at at at 
fh) 
= | frcae} 
= | | tote, m)exp lor -wr) dt \at | Sxx(@) dw 
—-o foo} 
= | Hx(o,-w)ox (w) dw (LE3 35) 
because | | ho(t1, T2) exp i(Wt2 — WT1)dt, dt2 = H2(w,-w) 
—-O —-O 
2. Cross correlation Ryx(tT); cross spectrum syy(@). 
For Ryx(t) = E[{¥(¢) — my} - X(t—1)] = E[Y(t) -X(¢—1)|—my E[X(t-7)], 
inserting Eq. 11.11 and E[X(t—t)] =0, yields 
= | Ay(t1)E|X(t —11) X(t -1) dr = | mucenrte—ner (11.34) 
—-o 
Therefore 
303 
