INPUT OUTPUT 
xe Ye 
LINEAR SYSTEM 
Fig. 2.28 Linear system. 
However, we had better treat g, for— © — + ©, because sometimes X, itself does 
not express the real cause of Y,, and g, can even be non—zero at t < 0. We assume, for the 
impulse response, 
> Igil < @. (2.162) 
Then 
Syy(@) = IG)? Sxx(@), (2.163) 
where 
G(@) = yy 81 € WT. (2.164) 
T=-0 
G(q) is called the transfer function or frequency response function of Y, to X;. For 
Syy(@) to be finite in total power | Syy(w)dw < ©, syy(w) must be a bounded function 
of w and | IG(@@) "dw < ©. Accordingly, by Parseval’s relation, 
Wigear< 00. 
Using Eq. 2.161 gives 
58 
Cc Temas | ce 
EE ee en | 
