1004 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



Ai, Ai , A5 , etc., will contribute a quadrature but no in-phase com- 

 ponent. It will be recognized from Fig. 42 that this is the same condition 

 as encountered in vestigial sideband transmission with pulses in the 

 latter case transmitted at intervals r = 7r/2cos = 1/4 /« . 



To realize the above condition ^nth pulses applied to a band-pass filter, 

 it is necessary that in (14.10) 



co^nr = n7r(>^ + N), (14.13) 



where N is an integer, or that 



^ = ^ = —77 — • (14.14) 



2com 4/„ 



The interval between pulses must thus be an integral number of half- 

 cycles plus one quarter cycle of the midband frequency /„ , as illustrated 

 for a particular case in Fig. 48. When /,„ is large in relation to the side- 

 band frequency this condition can be achieved with substantially the 

 same pulse spacing as ^^'ith vestigial sideband transmission. To secure 

 exactly the same rate of pulse transmission it is necessary that 



r = 1/4/., 



which, in conjunction with (14.14), gives 



N = h (fm/fs - 1). (14.15) 



Thus, if /,„ = 5fs , N = 2 and the interval r between pulses as obtained 

 from (14.14) is 1.25 cycles of fm . If fm = 10/^ , A^ = 4.5 and it is not 

 possible to have exactly the same pulsing rate as with vestigial sideband 

 transmission, since N must be an integer. It is then necessary to take 

 A^ = 4 or 5. With A" = 4 equation (14.14) gives r = 9/40/^ and with 

 A^ = 5, T = 11/40/s . This compares with r = 1/4/, = 10/40/, with 

 vestigial sideband transmission, so that there is a minor difference in 

 pulse intervals with the two methods. 



15. DOUBLE VERSUS VESTIGIAL SIDEBAND SYSTEMS 



From the preceding discussion it follows that, for the same bandwidth 

 and margin against interference from characteristic distortion, a two- 

 fold increase in transmission capacity can be approached with vestigial 

 over double sideband transmission. This assumes that the carrier is 

 transmitted at the proper level and that the phase characteristic is 

 linear, or that otherwise homodjnie detection is used to cancel the effect 

 of the quadrature component. 



