562 BELL SYSTEM TECHNICAL JOURNAL 



ments at precise instants are probably not realizable to a degree which 

 would keep the crosstalk within tolerable limits, so that one of the smooth 

 pulse shapes is preferred. Pulse 4 with a spacing of To is feasible from the 

 sampling precision point of view but a spacing of 2 To provides margin 

 against crosstalk arising from small imperfections in any realizable approxi- 

 mation to the theoretical pulse. 



It is to be noted that, if an instantaneous sample is taken of a PAM 

 pulse, the measured magnitude is affected directly by the instantaneous 

 value of noise present in the entire band occupied by the pulse. No fre- 

 quency selectivity can be applied afterward to remove the influence of any 

 part of the noise band because the error, even though caused by wide-band 

 components, is exactly the same as could have been produced by a uniquely 

 determined wave wholly confined to the signal band itself. The best 

 signal-to-noise ratio obtainable with instantaneous sampling is that asso- 

 ciated with minimum bandwidth for the pulse (i.e., pulse 9) and the corre- 

 sponding maximum stringency of synchronization requirements on the 

 sampling and pulse distortion. The same signal-to-noise ratio can, however, 

 be approached with a wider band provided that we allow a finite segment 

 of the received pulse to enter the channel filter. An averaging out of higher- 

 frequency disturbances produced by wide-band noise is thus attained. 



PCM. In PCM a short sample taken near the center of a pulse serves 

 to determine correctly the presence or absence of a pulse even in the presence 

 of interference at or near the breaking point of the sheer. Thus, pulse 4 

 may be used with a spacing of To , and if a gate pulse 25% of To is used, it 

 need not be aligned with an inordinate precision to obtain good operation.^^ 

 Greater tolerance in the matter of sampling would be obtained with pulse 2 

 but the frequency extravagance could scarcely be countenanced. As stated 

 we assume pulse 4 in our PCM bandwidth curves but employ pulse 11 in 

 Tables \T-\TII. Use of pulse 11 is a frequency conservation measure that 

 seems feasible only with PCM and is attractive only with binary PCM. 



Optimum Distribution of Selectivity Between Tr.\nsmitting and 



Receiving Filters 



In a regenerative repeater system both the receiving and transmitting 

 filters may be Gaussian without suffering cumulative narrowing of the system 

 bandwidth since each span commences with a freshly shaped pulse. In 

 this case, the transmitting filter of one repeater and the receiving filter of 

 the succeeding repeater combine, as Ciaussian filters do, to make anotlier 

 Gaussian filter. The resulting pulse may be one of the series 2 to 6 of Fig. 26. 

 On the assumption that one of these shapes is desired and that the trans- 



'' This is the pulse shape approximated in the experimental system described by 

 Meacham and Peterson (loc. cit.). 



