BACKGROUND NOISE IN BROADCASTING 335 



frequency output will be proportional to the audio-frequency compo- 

 nent of 



[E cos ut -\- N cos (co + n)ty-, 

 which is 



EN cos nt. (1) 



Now suppose that there is impressed, in addition to the desired 

 carrier and noise component, a weak carrier e cos (w + u)t. The sum 

 of the strong and weak carriers may be conveniently regarded as a 

 single wave of amplitude 



{E -\- e cos ut). 



This may be substituted for the amplitude E in (1), giving for the 

 noise output 



EN{1 -f K cos ut) cos nt (2) 



in which 



K = ejE. (3) 



The noise which is heard will consist of a steady portion, the amplitude 

 of which is proportional to EN, and another portion of variable ampli- 

 tude which is proportional to ENK cos ut. 



The factors that determine the importance of the flutter are many 

 and complex, but it seems likely that the most important of them is the 

 ratio of the variable component of the noise output to the steady com- 

 ponent. As long as the noise is loud enough to be obvious, this ratio 

 should be a fairly good measure of the perceptibility of the flutter, 

 and we shall venture to regard it as such. The experimental data to 

 be reported later will bear out this assumption. 



From (2) it is evident that the ratio mentioned is merely K, the 

 ratio of the amplitude of the interfering carrier to that of the desired 

 carrier. We shall call this ratio the "flutter factor" for the quadratic 

 detector and designate it by Fq. 



Fq^ K = e/E. (4) 



It is interesting that Fq is independent of the amplitude N of the high 

 frequency noise. 



It is possible to derive a similar factor, giving the ratio of the varia- 

 ble to the steady components of noise, for the linear detector. From 

 equations (70a) and (71) of the paper ^ already mentioned it follows 

 that the flutter factor for the linear detector, at low modulations of the 



desired wave, is 



Ne kK 



^^^lE^^X' ^^^ 



in which k = N/E. 



