. The Bell System technical journal . illustrated byconsidering the example in Section 14. For the optimum condition fx =, the margin is reduced by a factor and is thus For a quater-nary double sideband system the factor by which the margin is reducedis given by (), with g = 4 and with ^|:|P(n.)| + |F(-n.)|=^Efi-+E«-), where R{0) = , 2^^ = and X^~ = , as in the examplein Section 14. The reduction in margin thus obtained is M/Mmax = Hence the maximum tolerable interference for a quarternary doublesideband system is = as compared with for a bi
. The Bell System technical journal . illustrated byconsidering the example in Section 14. For the optimum condition fx =, the margin is reduced by a factor and is thus For a quater-nary double sideband system the factor by which the margin is reducedis given by (), with g = 4 and with ^|:|P(n.)| + |F(-n.)|=^Efi-+E«-), where R{0) = , 2^^ = and X^~ = , as in the examplein Section 14. The reduction in margin thus obtained is M/Mmax = Hence the maximum tolerable interference for a quarternary doublesideband system is = as compared with for a binaryvestigial sideband system under the optimum condition ^ = 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 pronouncedphase distortion, owing to the circumstance that a two-fold reductionin bandwidth with vestigial sideband transmission may afford a sub- --^-AMPLITUDE CHARACTERISTICS. FREQUENCY DELAY DISTORTION JMAX I MAX - CJmAX fwAX Fig. 49 — Comparison of double and vestigial side-band transmission in thepresence of delay distortion. THEORETICAL FUNDAMENTALS OF Pl^LSE TRANSMISSION 1007 stantial reduction in delay distortion over the transmission band. Thisis illustrated in Fig. 49, Avhere a variation in transmission delayis assumed. With a two-fold reduction in bandwidth, the productdmax/max for vcstigial sideband transmission is about 15 per cent of theproduct c/max/inax for doublc sideband transmission. Thus, with c?max/max= , dlnaxf max = 1-25, Corresponding to 6 = 5 radians, as assumed inthe example in Section 14. Vestigial sideband transmission is in this casefeasible with an adecjuate margin, about 40 per cent of the maximummargin in the absence of phase distortion. Double sideband transmissionwould not be possible, as is evident from Fig. 43, since it would be neces-sary to have c^max/max Icss thau 4
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