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BELL SYSTEM TECHNICAL JOURNAL 



This relation, which is true even if the noise band is not symmetrical about 

 }q, follows from equation (3.3-11) of Reference A. 



When Q y> rms In and/g is not at the center of the noise band it is easier 

 to obtain the asymptotic form of Nr from the approximation (3.6), 



R'^Q + Ic, 



instead of the double integral (4.7). When Q>> rms In and R is in the 

 neighborhood of Q (as it is most of the time in this case), Nr is approximately 

 equal to the expected number of times Ic increases through the value Ici = 

 R — Q \n one second. Thus, regarding 7c as a random noise current we 

 have from expression (3.3-14) of Reference A 



Nr ^ e~^?i^^^*»^ X [1/2 the expected number of zeros per second of I c] 

 and when we use equation (4.11) we obtain 



N, 



27r 



{h/b. 



Iir 



m-^v-aw (4_^2) 



Table 2 

 '(/) = wq = 6o//3 over a Band of Width jS 



Table 2 lists the forms assumed by (4.10) and (4.12) when the power spec- 

 trum w(j) of the noise current In is constant over a frequency band of width jS. 

 The quantity b^'m the expressions for bi represents the mean square value 

 oUn. 



In the general case where the band of noise is not centered on Jq and 

 where R is not large enough to make (4.12) valid we are obliged to return to 

 the double integral (4.7). Some simplification is possible, but not as much 

 as could be desired. Introducing the notation 



a = RQ/b,, y = b,Q{Bbo)-"- 



X = {boR' + biQsm e)(Bbo)-'i^ 



