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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



amplitude is ^ as compared to 14 for a quaternary system. If the phase 

 characteristic is linear and the carrier is transmitted at the optimum 

 level, or if homodyne detection is used, the effect of the quadrature com- 

 ponent is cancelled. The maximum tolerable interference is then l^ as 

 compared with ^^ for a quarternary double sideband system. 



In the presence of phase distortion, a substantial advantage can also 

 be realized with a binary vestigial system, which can be illustrated by 

 considering the example in Section 14. For the optimum condition fx = 

 0.4, the margin is reduced by a factor 0.4 and is thus 0.2. For a quater- 

 nary double sideband system the factor by which the margin is reduced 

 is given by (13.07), with g = 4 and with 



^|:|P(n.)| + |F(-n.)|=^Efi-+E«-), 



where R{0) = 0.97, 2^^ = 0.13 and X^~ = 0.09, as in the example 

 in Section 14. The reduction in margin thus obtained is M/Mmax = 

 0.32. Hence the maximum tolerable interference for a quarternary double 

 sideband system is 0.32/6 = 0.053 as compared with 0.20 for a binary 

 vestigial sideband system under the optimum condition ^ = 0.4. 



For the same transmission capacity and same number of pulse ampli- 

 tudes, a substantial transmission advantage may be realized with ves- 

 tigial over double sideband transmission in circuits with pronounced 

 phase distortion, owing to the circumstance that a two-fold reduction 

 in bandwidth with vestigial sideband transmission may afford a sub- 



--^-AMPLITUDE CHARACTERISTICS 



FREQUENCY 



DELAY DISTORTION 



JMAX I MAX - 0.15 CJmAX fwAX 



Fig. 49 — Comparison of double and vestigial side-band transmission in the 

 presence of delay distortion. 



