718 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Another point brought out by these tests was that the difficulty or ease 

 with which the difference between the two systems could be detected was 

 substantially independent of speech volume. 



Noise Ad.antage 



The value of S/Nr given above may be used to evaluate the noise ad- 

 vantage. Basically the problem is to find the permissible db increase in 

 noise at the output of the transmission medium when the PAM system of 

 Fig. 1 is equipped with an instantaneous compandor instead of linear net- 

 works having characteristics indicated by the dotted line in Fig. 4. For the 

 comparison to be valid, the noise at the output of the system during intervals 

 when the signal voltage is zero must be the same for the two conditions, 

 and when the compandor is used S/Nr must equal 22 db. 



Recall that Vr represents the rms value of the noise voltage at the output 

 of the transmitting medium when the instantaneous compandor is used, 

 and let Vr represent the corresponding value when the linear networks are 

 used. The noise susceptibility of the linear system is unity. Therefore, the 

 noise at the output of the system during intervals when the signal voltage 

 is zero will be the same for the two conditions provided Vr = Vr Sz. When S3 

 is replaced by its value in (14) we require that 



r, = |. (15) 



The equation which specifies that S/Nr equals 22 db is 



Vt 

 12.59 = — (16) 



obtained by replacing S/Nr in (13) with the voltage ratio corresponding to 

 22 db. As shown by the lower curve of Fig. 6, Vt is a function of the ex- 

 pansion ratio, K. The quality of the two systems will be the same provided 

 (15) and (16) are satisfied simultaneously. 



Values of Vr, Vr, and K which simultaneously satisfy (15) and (16) are 

 plotted in Fig. 8. Larger values of K would yield values of S/Nr smaller than 

 the specified value of 12.59 db. Smaller values of K correspond to less noise 

 improvement and make S/Nr larger than assumed necessary. The use of 

 these curves will be illustrated by the following example. 



It will be assumed that the rms value of the noise voltage at the output 

 of a typical telephone channel is approximately 56 db below the hghest signal 

 voltage which the system is called upon to transmit. In the PAM system of 

 Fig. 1 one volt was arbitrarily taken as the peak signal voltage at the output of 

 the transmitting medium so that Vr is 56 db below one volt. From the upper 



