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BELL SYSTEM TECHNICAL JOURNAL 



I 



Here, in the factor {^Wc^ + W), the term W is predominant. The 

 eUmination of the term coi^ has resulted in a substantial reduction in 

 the noise power. 



Returning to the general formula (66) for Pu, it is clear, that, if in 

 addition to eliminating the term coi^, the parameter v = ;u/X can be 

 made equal to — 1, the noise power will be reduced to its lowest 

 limits: 



Pn = lo^JN'. 



This highly desirable result can be effected by amplitude limitation, 

 the theory of which will now be discussed. 



V 



When amplitude limitation is employed in frequency-modulation, 

 the incoming high frequency signal is drastically reduced in amplitude. 

 If no interference is present this merely results in an equal reduction 

 in the low frequency recovered signal which is per se undesirable. 

 When, however, noise or interference is present, amplitude limitation 

 prevents the interference from affecting the amplitude of the resultant 

 high frequency wave; its effect then can appear only as variations in 

 the phase or instantaneous frequency of the high frequency wave. To 

 this fact is to be ascribed the potential superiority of frequency- 

 modulation as regards the reduction of noise power. This superiority 

 is only possible with wide band high frequency transmission ; that is, 

 the index of frequency-modulation X must be large compared with the 

 low frequency band width coa- Insofar as the present paper is con- 

 cerned, the potential superiority of frequency-modulation with ampli- 

 tude limitation is demonstrated only for the case where the high fre- 

 quency noise is small compared with the high frequency signal wave. 



^f 



Jo 

 -\- iojnt -\- dn), the re- 



If, to the frequency-modulated wave exp I i 



Qdt 



there 



added the typical noise element A „ exp (iw 

 sultant wave may be written as 



exp(i f ^dtyll + Anexp (i C Uji jj . (71) 



Postulating that ^ „ ^ 1 and therefore neglecting terms in A n^, 

 the real part of (71) is 



1 + ^rt cos ( r ^ndt j Vcos (I ndt + An sin I C Undt j j . (72) 



