94 



BELL SYSTEM TECHNICAL JOURNAL 



Thiede has studied the mean square value of the fluctuations of the 

 integral 



A{t) = f l\r)e-"''-'UT 



(3.9-22) 



The reading of a hot wire ammeter through which a current / is passing is 

 proportional to A{t). a is a constant of the meter. Here we study A{t) by 



5 6 8 10 



30 40 50 60 



Fig. 5* — Filtered thermal noise — spread of energy fluctuation 



•''1 



P{t) dt, li random, / is noise current. 



^'i = Ejb/E.io , y2 = E.2i/E.io ■ 

 fb — fa = band width of filter. 



first obtaining its correlation function. This method of approach enables 

 us to extend Thiede's results 



The distributed portion of the power spectrum of A(t) is given by (3.9- 

 30). When the power spectrum w(f) of /(/) is zero except over the band 

 fa < f < fb where it is Wo , the power spectrum of A (t) is 



and is zero iromfb — fa up to 2/o . The spectrum from 2fa to 2fb is not zero, 

 and may be obtained from (3.9-34). The mean square fluctuation of A{t) 

 is given, in the general case, by (3.9-28) and (3.9-32). For the band pass 

 case, when (/& — fa)/oi is large, 



r.m.s, 



Ajt) - A 

 A 



[-J1/2 

 2(/6-/a)j 



5 Elec. Nachr. Tek., U (1936), 84-95. This is an excellent article. 

 Note added in proof. The value of >'2 at should be .415 instead of .403. 



