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BELL SYSTEM TECHNICAL JOURNAL 



Figure 3 shows the curve of admittance vs. frequency required for on-and- 

 ofif and plus-and-minus switching. Referred to the mid-band admittance as 

 unity, the admittance is reduced to one-half (six db loss) at the frequencies 

 rNq/2 and (r + 2)Nq/2 which are the nominal upper and lower cutoffs. 

 TV is an even integer and r is zero or any positive integer. The admittance 

 curve has odd-symmetry about the cutoff frequencies — that is, if at a 

 frequency x cycles below a cutoff frequency, the admittance has the value a, 

 it must be 1 — a at a frequency x cycles above the cutoff. The nominal 



ADMITTANCE OF REQUIRED FILTER 



(^-0<i ^ (^+')a 



['-^^M-Oa '^^N, [qiiN.,]a 



(rN-3)^ (rN-i)^ (rN + i )| (rN+3)^ [(r+2)N-i]f [(r+2)N+l]| [(r+2)N+3]f 



FREQUENCY 

 N = 2,4,6 r = l,2,3 



Fig. 3 — Vestigial sideband transmission in time division multiplex systems 



band transmitted in the case of on-and-off switching consists of the upper 

 sideband on the harmonic rNq/2, the lower sideband on the harmonic 

 (r -{- 2)Nq/2, and all intervening sidebands. In the case of plus-and-minus 

 switching the upper and lower sidebands on frequencies {rN -\- \)q/2 to 

 [{r -\- 2)N — l]q/2 inclusive are transmitted. Impairment of the nominal 

 band by the filter is made up by transmitting the appropriate parts of 

 sidebands outside the nominal range. It is easily verified that either of the 

 systems depicted in Fig. 3 satisfies the required conditions for multiplex 

 transmission without interchannel interference when the sidebands produced 

 by a given signal have equal amplitudes over the range utilized. 



