u\ 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



overlaps resulting from a low-frequency cut-off, as illustrated in Fig. 

 35, and in peak intersymbol interference. 



If AP(0 = P(0 — -Po(0 is the modification in the impulse characteris- 

 tic shown in Fig. 32, the modification in the dipulse transmission charac- 

 teristic resulting from a low-frequency cut-off becomes 



AiP(0 = AP(0 - AP(^ - n) 



(9.07) 



where ti is the interval between the positive and negative dipulse com- 

 ponents. 



The difference given by (9.07) represents the differential in the curve 

 Pit) — Po(t) shown in Fig. 32 over an interval ri . It can be shown that 

 the maximum cumulative effect or peak intersymbol interference for a 

 long pulse train is represented by the sum of the differentials given by 

 (9.07) and is approximately equal to 



U ^ AP(ri) = P(ri) - Po(ri). 



(9.08) 



As an example, if the shape of A — Ao in Fig. 32 were about the same 

 as that of .4o , AP(t) would have the same shape as Po(t) but would be 

 lower in peak amplitude by the factor /o//i and would have the time 

 scale increased by the factor fi/fo . Peak intersymbol interference as 



AP(t)-AP(t-7; 



AP(t) 



AP(t-7i) 



-^ ^ k 



Fig. 35 — Low-frequency cut-off effects AP(t) and AP(t — n) for positive and 

 negative pulses and resultant effect AiP(t) = AP(t) — SP{t — n) for a dipulse. 



