INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



695 



34 

 32 

 30 



SIGNAL POWER IN DECI 

 5 10 15 20 



BELS BELOW FULL LOAD SINUSOID 

 25 30 35 40 45 50 



O 28 



? 



O 

 a. 



a. 

 O 

 cr 

 a: 



UJ 



O 



z 



isl 



t- 



z 

 < 



D 

 O 



26 

 24 

 22 

 20 

 18 

 16 

 14 



< 



Z 



10 



6 8 10 



>0 40 60 



C 



100 200 400 600 1000 



Fig. 19 — Signal to quantizing error power ratios (in db) as a function of rela- 

 tive signal power for companding corresponding to ju = 100 and 1,000 when n = 7 

 digits per code group and a dc component corresponding to B = 100 is present in 

 the signal. The influence of the dc component may be judged by comparing these 

 curves with those shown in Figs. 15 and 18 for n = 7. Corresponding results for dif- 

 ferent values of n may be derived bj- the addition or subtraction of appropriate 

 multiples of 6 db from each ordinate. 



of virtually all the anticipated companding improvement for weak 

 signals. 



(6) Background Noise Level. We have already noted the probable 

 futility of increasing the signal to cjuantizing error power ratio consider- 

 ably beyond that value which is subjectively equivalent to the antici- 

 pated ratio of signal to background noise from other sources. 



If the subjective relation between quantizing error power and noise 

 power were known, the curves in Figs. 15 to 19 could be redra^Mi for 

 meaningful comparison with ratios of signal to backgroimd noise. In 

 the absence of such information, we shall assume as a first approxima- 

 tion, that noise and quantizing error power are directl}^ comparable.* 



Suppose that we set an upper limit on the background noise by con- 



* The similarity between noise and ciuantizing error power has often been 

 noted. For example, one may consult references 2, 6 and 12 as well as Appendix I 

 on "Noise in PCM Circuits" in Reference 11. The assumption of direct com- 

 parabilit}' is also to be found in Reference 4. 



