1002 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



pulse amplitudes becomes: 



Ml. 



Thus, for an ideal impulse characteristic as assumed above, the 

 quadrature component gives rise to 50 per cent maximum intersymbol 

 with fji = 0, and to negligible intersymbol interference when /x = 0.8 or 

 greater. By way of comparison, the margin would be zero with double 

 sideband transmission at the rate assumed above, i.e., twice the normal 

 double sideband rate. This follows from (13.07) when it is considered 

 that P{zkT) = }4 P(0), P(±2t) = 0, so that the sum of the absolute 

 values of the impulse characteristic at the sampling points is equal to 

 P(0) and thus M/ikfmax = 0. 



Elimination of the effect of the quadrature component by the above 

 method is contingent on a symmetrical impulse characteristic, i.e., 

 P{nT) = P{ — nT), a condition which can be realized only with a linear 

 phase shift. Furthermore, the in-phase components must vanish at the 

 sampling points, which entails an ideal amplitude characteristic. In the 

 presence of phase distortion the effect of the quadrature component 

 cannot be eliminated but may be reduced by proper choice of the ratio 

 ju, as discussed below for a transmission characteristic with moderate 

 phase distortion. 



As an example consider an impulse characteristic as shown in Fig. 23 

 for h = 5 radians. The in-phase and quadrature components at the 

 various sampling points are in this case 



R{0) = 0.97 R{-2t) = -0.09 R(2r) = 0.13 



P(-4r)^0 P(4r)^0 



Q(-t) = -0.54 Q(t) = 0.44 



Q(-3r) ^0 Q(Zt) = -0.03 



Q(-5t)^0 Q(5r)^0 

 Hence 



2;P+ = 0.13 ^R~ = 0.09 SQ"^ = 0.44 ^Q" = 0.57 

 Equation (14.08) in this case becomes 



ilfi = -J— ((0.88' + 0.13V)'" - [(0.97m + 0.13)' 



1 — M 



+ (0.57 - 0.44m) Y''). 



