1G SG eINGES ot Xan ceINh | (2.169) 
—-co 
X, Y, , 
————| _ LINEAR SYSTEM YK 
Fig. 2.29. Linear system in the presence of noise. 
Then, 
Ry'x(r) = E[X# Yr] 
= > gr EIX# Xtra] + EX# Nc] i) 
T=-—0 
ad Ss &r Rr ire a) 
T=—-O 
because, 
E[X# Ni] = 0. (2.171) 
Therefore 
1 co : fo °} 
sy x) = Sa SS Bee G 2) 
r=-@ t=-@ 
= G@W)sxx(@) = Syx(@) (2.172) 
and 
60 
