896 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



tered on the pulse repetition frequency. This possibility resides in the 

 circumstance that a random "on-off" pulse train can be resolved into 

 two components. One is an infinite sequence of pulses of the same 

 polarity and equal amplitude, the other a sequence of randomly positive 

 and negative polarity. The response of a resonant circuit to the first 

 component is a steady state sinusoidal wave of the pulse repetition fre- 

 quency. The second component gives rise to random variations in ampli- 

 tude and phase, which in principle can be limited to anj^ desired extent 

 by limiting the band of the resonant circuit and the deviation in the 

 resonant frequency from the pulse repetition frequency. 



A principal feature of this method of "self -timing", aside from its 

 simplicity, is that the timing wave becomes a slave of the pulse train. 

 Thus, if there is a fixed delay in pulse regeneration at a repeater, the 

 same delay is imparted to the timing wave derived from the pulse train 

 at the next repeater. This prevents a cumulation of such fixed delay.^ 

 with respect to the timing wave, but not with respect to an absolute 

 time scale; i.e., with respect to an ideal timing wave transmitted along 

 the repeater chain and independent of the pulse train. 



1.5 Self -Timed Repeaters with Partial Retiming 



A timing wave derived from the pulse train with the aid of a resonant 

 circuit can be used in conjunction with complete or partial retiming. 

 With complete retiming, pulses could be regenerated at the zero points 

 in the timing wave, and the effects of amplitude variations in the timing 

 wave can thus be avoided. Timing deviations in the regenerated pulses 

 would in this case depend only on phase deviations in the timing wave, 

 caused partly by the component of randomly positive and negative 

 polarity in the pulse train and parth' by timing deviations in the pulse 

 train from which the timing wave is derived. 



With partial retiming the situation is more complex. Timing de^•ia- 

 tions in regenerated pulses in this case depend not only on amplitude 

 and phase variations in the timing wave, but also on the regeneration 

 characteristics of the repeaters. 



1 .6 Types of Timing Deviations 



In a regenerated pulse train there will be fixed and random timing 

 deviations. Of the latter there are three types. One is the timing devia- 

 tion taken in relation to an exact timing wave with a period T equal to 

 the nominal pulse interval. The second is the timing deviation taken in 

 relation to the timing wave derived from the pulse train, which in itself 



