. The Bell System technical journal . tted, the minimum value ofthe envelope is obtained by considering the maximum negative overlapsof the in-phase components, in conjunction with the minimum value ofthe quadrature component, which gives Wmin = [(Amax i^(0) Amax Z^) + ^^min (ZQ The margin for distinction between Am in and A max is M = TFmin — and becomes M = Amax [{R(o) - ZRy + ahq- - ZQ-yf () - Amax [{HR(0) + Z^^) + (ZQ - f^ZQyf, where THEORETICAL OF IULSE TRANSMISSION 1001 The margin for a unit dilference A^ax — -Imi,, , i-c. Mi = M/(A,■ -Imill) becomes: 1 — M (
. The Bell System technical journal . tted, the minimum value ofthe envelope is obtained by considering the maximum negative overlapsof the in-phase components, in conjunction with the minimum value ofthe quadrature component, which gives Wmin = [(Amax i^(0) Amax Z^) + ^^min (ZQ The margin for distinction between Am in and A max is M = TFmin — and becomes M = Amax [{R(o) - ZRy + ahq- - ZQ-yf () - Amax [{HR(0) + Z^^) + (ZQ - f^ZQyf, where THEORETICAL OF IULSE TRANSMISSION 1001 The margin for a unit dilference A^ax — -Imi,, , i-c. Mi = M/(A,■ -Imill) becomes: 1 — M () The s{)ecial case of an ideal transmission characteristic as sliown inFig. 47 will be considered first. In this case 72(0) = 1 R{2t) = 0 R{-2t) = 0 R{) = 0 A(-4r) = 0 Qir) = Q(-r) = (KSt) = 0 Q(-3t) = 0 so that: 1:^+ = 0 X^~ = 0 Z^ = DQ- = () in this case simplifies to Ml 1 - 1 - m + ^ (1 - m) ni/2 () For various values of |U = ^4niinAlmax the margin for luiit (hffer ence m ENVELOPE Pit). ^ 1 ~-A P(o) = P(rj = P{2T) = 0 P(37-) = 0 Fig. 47 — Envelope of idealized impulse characteristic. 1002 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 pulse amplitudes becomes: Ml. 0 Thus, for an ideal impulse characteristic as assumed above, thequadrature component gives rise to 50 per cent maximum intersymbolwith fji = 0, and to negligible intersymbol interference when /x = orgreater. By way of comparison, the margin would be zero with doublesideband transmission at the rate assumed above, , twice the normaldouble sideband rate. This follows from () when it is consideredthat P{zkT) = }4 P(0), P(±2t) = 0, so that the sum of the absolutevalues of the impulse characteristic at the sampling points is equal toP(0) and thus M/ikfmax = 0. Elimination of the effect of the quadrature component by the abovemethod is contingent on a symmetrical impulse characteristic, ,P{n
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