subsections and assuming the existence of a spectrum of X(t), Y(r) and a Fourier trans- 
form of g(u), 
Syy(@) = |IG@)?sxx(w), (2.120) 
G(w) = | g(t)e "dr. (2.121) 
A few samples of simple and ideal filters are given as follows: 
1. Band—pass filter (Fig. 2.22) 
G (w) 
Wo -w, (0) w, OW — @® 
Fig. 2.22. Band—pass filter. 
1 ; fora, < lol < a2 
IG@)? = (2.122) 
otherwise 
Then 
lee) @2 
g(t) = uN G(w)e'dw = as | eda 
2 2 
—-3o @, 
SiN WoT — SiIN@ T 
= oe ee) forall’r. (2.123) 
aT 
From the form of this function and Eq. 2.119, we need the input process X(t) for 
— © <t< ©, so theoretically this filter is physically unrealizable. 
49 
