692 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



in 



eg 

 o 



LU 

 Q 



36 

 34 

 32 

 30 

 28 

 26 

 24 

 22 



SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 

 5 10 15 20 25 30 35 40 45 50 



20 



2 

 N 18 



16 



Z 

 < 



3 

 O 



O 14 



< 



Z 



12 

 10 



8 



I 



8 10 



20 



40 60 



100 



200 



400 600 1000 



C 



Fig. 16 — Signal to quantizing error power ratios (in db) as a function of rela- 

 tive signal power for companding corresponding to /i = 200. Sj-mbols have the 

 same significance as in Fig. 15. B = « throughout. 



which have been established for conventional noise and distortion. If 

 these were available, graphs such as those in Figs. 15 to 18 could be 

 used to select the proper number of digits to be used ^^ith various de- 

 grees of compression. In the absence of such information Ave shall com- 

 plete this illustrative study b}^ adopting a signal to ciuantizing error 

 power ratio of at least 20 db as a tentative standard of adequate per- 

 formance at all volumes.* 



Figs. 15 and 16 show that seven digits (i.e., 2' = 128 tapered quantiz- 

 ing steps) and n = 150 will meet this objective. Furthermore Figs. 17 

 and 18 indicate that six digits (2 = 64 tapered steps) would suffice 

 provided (38) is replaced by the more stringent limitation. 



500 <M< 1,000 



(40) 



* This value does not appear unreasonable, as a first approximation, in terms 

 of experience with noise and harmonic distortion. 



