990 THE BKLL SYSTEM TECHNICAL JOURNAL, JULY 1954 



of an unbalanced system, only the balanced component need to be con- 

 sidered in evaluating rms intersymbol interference, which will thus be 

 the same whether or not the system is balanced. As shown previously, 

 peak intersymbol interference, or the margin for distinction between 

 pulse amphtudes, depends only on the peak to peak pulse excursion and 

 is thus the same for unbalanced as for balanced systems. It may be 

 noted here that for a balanced system the transmitted power is a mini- 

 mum for a gi^^en margin in pulse reception, as is the interference in other 

 systems that may be caused by the transmitted pulses. 



For a symmetrical band-pass system, rather than a low-pass system 

 as discussed above, Qinr) = in (12.08). The envelope of the pulse 

 train then becomes 



00 



TF(0) = E AnRM, (13.15) 



71= — 00 



where Rinr) = R-inr) -\- R+inr) = 2R+(nT), with R^ and R+ given by 

 (2.10). 



Since (13.15) is of the same form as (13.01), the relationships estab- 

 lished above for low-pass systems also apply to symmetrical band-pass 

 systems, with Ri^nr) replacing Pinr). Rinr) will have the same shape as 

 Pint), but will be greater by a factor 2, which will appear as a multiplier 

 in the various expressions and hence not alter the requirements on toler- 

 able pulse distortion or intersymbol interference. 



14. TRANSMISSION LIMITATIONS IN ASYMMETRICAL SIDEBAND SYSTEMS 



The formulation of transmission limitations imposed by pulse distor- 

 tion in asjrmmetrical sideband systems is complicated by the presence 

 of the quadrature component in the impulse transmission characteristic. 

 Of particular interest are the transmission limitations with vestigial 

 sideband as compared with double sideband transmission, assuming the 

 same bandpass characteristic in both cases, a question which has been 

 dealt with in literature for systems with a linear phase characteristic .' 

 Relationships (2.18) and (2.19) facihtate a comparison also for systems 

 with phase distortion, as shown in the following. 



If the envelope of the impulse characteristic with double sideband 

 transmission is P{t), the in-phase and quadrature components with 

 vestigial sideband transmission are given by (2.19), with coy = cos or 



R = R^ -{- R+ = cos (i^st - rps) P(t), 



(14.01) 

 Q = Q_ - Q+ = sin (o^st - ^s) P{t). 



