VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 525 



The first term, 



ojc exp ( icoj + i\ I sdt) , (45) 



is still a pure frequency modulated wave. The second term, 



\s(t) -exp ( iooj + ^'X I sdt), (46) 



is a "hybrid" modulated wave, since it is modulated with respect to 

 both amplitude and frequency. The important point to observe is 

 that, by differentiation, we have "rendered explicit" the wanted low 

 frequency signal. We infer from this that the detection of a pure 

 frequency modulated wave involves in effect its differentiation. The 

 process of rendering explicit the low frequency signal has been termed 

 "frequency detection." Actually it converts the pure frequency 

 modulated wave into a hybrid modulated wave. 



Every frequency distorting transducer inherently introduces fre- 

 quency detection or "hybridization " of the pure frequency-modulated 

 wave, as may be seen from formula (16). The transmitted current is 

 conveniently written in the form 



I = Y{icoc) exp(i f'2dt)-ll+ — \s-\-^,-\c2 



('X'""')-! 



COi 2 ! C02 



where 



(Note that w„ has the dimensions of frequency. It may be and usually 

 is complex.) 



Every term in (47) except the first, is a hybrid modulated wave. 



In passing it is interesting to compare the distortion, as given by 

 (47), undergone by the pure frequency-modulated wave, with that suf- 

 fered by the pure amplitude-modulated wave (39), in passing through 

 the same transducer. The transmitted current corresponding to the 

 amplitude-modulated wave (39) is 



1 ds . 1 d^s 



1= F(ico,)e-='|5(/)+4-^ + 



iwidt 2 !(*'co2)^ dt^ 



+jihf%+---^- («' 



