THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 773 



9. TRANSMISSION DISTORTION BY LOW FREQUENCY CUT-OFF 



A low-frequency cut-off in the transmission frequency characteristic 

 of wire systems is unavoidable with transformers as employed for in- 

 creased transmission efficiency or other reasons. In single sideband 

 frequency division systems, there is a low-frequency cut-off in individual 

 channels caused by elimination of the carrier and part of the desired 

 sideband. The effect of a low-frequency cut-off can be avoided by em- 

 plojdng a symmetrical l)an(l-pass characteristic as illustrated in Fig. IG, 

 or more generally by double sideband transmission with a two-fold in- 

 crease in bandwidth as compared to a low-pass system. It can also be 

 overcome by vestigial sideband transmission with inappreciable band- 

 width penalty, but with complications in terminal instrumentation. The 

 effect of a low-frequency cut-off can, furthermore, be reduced without 

 frequency translation as involved in double or vestigial sideband trans- 

 mission, by certain methods of shaping or transmission of pulses, as 

 discussed in the following, and by certain methods of compensation at 

 the receiving end or at points of pulse regeneration not considered here. 



The nature of the pulse distortion resulting from a low-frequency cut- 

 off is illustrated in Fig. 32. If the phase characteristic is assumed linear, 

 the amplitude characteristic may be regarded as made up of two com- 

 ponents, in accordance with the following identity: 



A(co) = Ao(a:) + [A(co) - A^], (9.01) 



where ^4o(a;) is the amphtude characteristic without a low-frequency 

 cut-off and [A((j}) — Ao(co)] a supplementary characteristic of negative 

 amplitude, as indicated in Fig. 32. 



The impulse characteristic may correspondingly be written 



P(t) = Po(0 + [^(0 - Po(t)]. (9.02) 



If the cut-off is confined to rather low frequencies, the impulse charac- 

 teristic AP{t) = P(t) — Po{t) will extend over time intervals substan- 

 tially longer than the duration of Po(t) or the interval at which pulses 

 are transmitted. The total area under the resultant pulse is always 

 zero. 



When a sufficiently long sequence of pulses of one polarity is trans- 

 mitted, the cumulative effect of the pulse overlaps resulting from the 

 modification P(t) — Po(t) in the impulse characteristic will be a dis- 

 placement of the received pulse train, as illustrated in Fig. 33 for various 

 intervals between the pulses. This apparent displacement of the zero 

 line, often referred to as "zero wander," will reduce the margin for dis- 



