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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



pulse overlapping into the middle pulse. The instantaneous amplitude 

 of the received train at a time to referred to the peak amplitude of the 

 middle pulse is 



W{U) = A.,Pito - r) + AoPito) + AiP{to + r), 



1 



I 



n=-l 



= tl AnPito + nr). 



(12.01) 



When the sequence of pulses transmitted at uniform intervals r extends 

 between n = — <x> and <x> , the instantaneous amplitude of the pulse 

 train at time to is 



TF(/o) = Z AnPHo + nr). 



(12.02) 



The above equation gives the instantaneous value W(to) for any se- 

 lected combination of transmitted pulses. The transmitted pulses may 

 have any value within certain limits, as when they represent signal 

 samples in a pulse amplitude modulation system, or may assume two or 



AMPLITUDES OF TRANSMITTED PULSES 

 Ao 



Ai 



<J,W{t) 



IMPULSE TRANSMISSION 

 CHARACTERISTIC 



-*^ t H- 



W(t) = A-iPtt+r)+AoP(t) + AiP(t-7-) 



Fig. 42 — Formulation of expression for pulse train envelope in terms of im- 

 pulse characteristic and amplitudes of transmitted pulses. 



