710 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



particular pulse may be represented as Fi + ?^i, where Vi corresponds to the 

 signal voltage and vi to the noise voltage This pulse is impressed upon the 

 input of a wide-band expandor (Fig. 4) and produces a new pulse at the 

 output of the expandor. It will be assumed throughout that the maximum 

 values of expandoi input and output voltages are equal, and for convenience 

 will be taken as unity. The solid curve is the positive portion of an assumed 

 expandor characteristic. Since Vi represents the magnitude that the input 

 pulse would have if the noise voltage were zero, Ei repiesents the corre- 

 sponding magnitude of the output pulse. When the effect of noise is taken 

 into account, the magnitude of the output pulse is £i + A£i. This goes by 

 way of the sampler and distributor to the input of Fz. 



V, V,+v, 



INPUT VOLTAGE 



Fig. 4 — Instantaneous expandor. 



From the sampUng principle one deduces^'^ that each pulse which appears 

 at the input to Fa is directly proportional to the signal which occurs A/ 

 seconds later at the output, where A/ is the delay in Fz. This delay will be 

 neglected. Thus, in response to Ei + A£i at the input, the value of the 

 voltage at the output of Fz is k{Ex + AjEi) where k depends upon the design 

 details of the system. Represent instantaneous signal and noise voltages at 

 the output of Fz by S\ and iVi. Then, 



S, = kE, (1) 



and 





(2) 



