526 BELL SYSTEM TECHNICAL JOURNAL 



This equation corresponds to (47) for the pure frequency-modulated 



wave. 



Ill 



In this section we consider the recovery of the wanted low frequency 

 signal s{t) from the frequency-modulated wave. This involves two 

 distinct processes: (1) rendering explicit the low frequency signal 

 "implicit" in the high frequency wave; that is, "frequency detection" 

 or "hybridization" of the high frequency wave; and (2) detection 

 proper. 



It is convenient and involves no loss of essential generality to 

 suppose that the transducer proper is equalized in the neighborhood of 

 the carrier frequency Wc\ that is, 



-^Yiic,.), ^F(ico.), ••• (50) 



acoc acoc 



are negligible. 



Frequency detection is then effected by a terminal network. We 



therefore take as the over-all transfer admittance 



yM-Y{io:). (51) 



y{icio) represents the terminal receiving network; it is under control and 



can be designed for the most efficient performance of its function. As 



we shall see, it should approximate as closely as possible a pure reactance. 



Taking the over-all transfer admittance as (51), we have from (47), 



/ = yiiwc) Y(icoc)-exp i i \ 



^dt 



K . 1 



X 1 +-X5-f ;^T— ,C2+T1— ,^3 + 



Oil 2 \(jii 



|. (52) 



where now 



1 f/" 



y[i(jic) d(jOc 



Inspection of (52) shows that the terms beyond the second simply 

 represent distortion. The terminal network or frequency detector 

 should be so designed as to make the series 



i+A + (Ay + (A)'+... 



rapidly convergent from the start.^ In fact the ideal frequency de- 

 tector is a network whose admittance y{io)) can be represented with 



^ See note at end of this section (p. 528) for specific example. 



