690 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



bounds oi' all these regions (see Figs. 10 to 13) are approximately (loinci- 

 dent (for 100 ^ m /^ 1,000), the advantage of increasing /x substantially 

 beyond 100 will depend largely on the expectation of encountering values 

 of Co -^ (TV1,000) with .sufficient frequency in the various channels 

 served by the common compressor. 



These arguments may of course be applied, with suitable modifications 

 depending on the range of C, n, and B values requiring attention, to any 

 effect capable of formal description in terms of an effective dc bias super- 

 imposed on the signal input to the compressor. 



(b) Backgrotmd Noise Level. It does not seem reasonable to strive for 

 an increase of the signal to quantizing error power ratio substantially 

 beyond that value which is subjectively equivalent to the anticipated 

 ratio of signal to background noise from other sources. 



Since the quantizing error power depends on the number of digits 

 per code group, the comparison of ciuantizing error power and noise 

 power is reserved for subsequent discussion of the reciuired number of 

 quantizing steps. It will be noted that the comparison must remain 

 somewhat speculative in the absence of a determination of the subjective 

 equivalence of quantizing error power and noise. 



C. Choice of the Number of Digits Per Code Group 

 1 . Ideal Behavior for Speech 



As previously remarked, the number of quantizing steps will deter- 

 mine the ratio of signal to quantizing error power to which the com- 

 panding improvement is to be added. Since the quantizing error power 

 is inversely proportional to N' = 2 ", this power will be reduced by 6 

 db for each additional digit. Comparison of this (5 db per digit improve- 

 ment with the roughly 24 to 35 db improvement corresponding to weak 

 signals in Fig. 8 (for 100 ^ m ^ 1,000) reveals that, for such sig7ials, 

 companding is equivalent to the addition of four to six digits per cede group, 

 i.e., to an increase in the mimber of quantizing steps by a factor between 

 2* = 16 and 2^ = 61^. This equivalence is portrayed in Fig. 9. Our failure 

 to realize a companding improvement of about -43 db as predicted for 

 \x. = 1,000 in Fig. 9 may be traced to the fact that the weakest signals 

 now under consideration are not sufficiently weak to be confined to the 

 linear region (e/V) « ijT^) of the /x = 1,000 characteristic. This is re- 

 flected in the unsaturated improvement exhibited in Fig. S for the 

 weakest signals when /x = 1 ,000. 



Although it is clearly preferable to suppress (luantizing error power 

 by companding rather than by inci'easing the number of ([uantizing 



