934 THE BELL SYSTEM TECHNICAL JOURNAL, JILY 1057 



where 



A^ = cos 2,^(1 - cos 2AcoTe~"'''"'"=') + sin 2^ sin 2AcoTe~"'''"-'^, (29) 

 2) = 1 + e-2"or/Q _ 2g-"o^/Q p^jg 2Acor. (30) 



With the same approximations as used previously in connection with 

 (12) and with 



cos 2AcoT ^ 1 - 2(Acor); sin 2Acor ^ 2AcoT, 



iV^|, (31) 



D ^ (^ly [1 + n (32) 



1 _ e-"or/Q ^ 2x/Q. (33) 



With these approximations in (27) and (28), 



a; ^ ^ (I)'" [1 - ^V21'", (34) 



which apply when }p is small and (27r/Q) « 1 . 



6. Response to Random Dipulse Train 



Each dipulse is assumed to consist of two impulses of unit amplitude 

 and opposite polarity, displaced by an interval 5, which in general will 

 be a function of the pulse position; i.e., 5 = d{n). The response of the 

 resonant circuit to a train of such dipulses, obtained by taking the dif- 

 ference in response to the two impulses, is given by 



.V 



A,{t) = P(0) 



cos oiaij, — nJ )e 



(36) 

 — cos oiM — nl + b[ri)\e 



In determining the response, mistuning of the resonant current can be 

 disregarded; i.e., coo = co. Furthermore, in the second term of (36) it is 

 permissible to take 



exp [-wo5(n)/2Q] ^ 1. 



