INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



693 



2. Practical Limitations 



(a) Mistnatch Between Zero Levels of Signal and Compandor. From 

 the previous discussion of the effect of Co on the choice of n, it is clear 

 that, if B can be confined to the vicinity of 1,000, the analysis of the 

 required number of digits in the absence of instability (B = <x>) may 

 be applied. 



On the other hand, behavior for B = 100 may be judged from the 

 plot of signal to quantizing error power ratio versus signal power for 

 ju = 100 and 1,000 (with seven digits) shown in Fig. 19. Since this ratio 

 now fails to exceed about 16 db for the weakest signals of interest, we 

 conclude that an increase to eight digits (2 = 256 tapered steps), with 

 a concomitant 6 db improvement for all signals, is required to meet our 

 20 db objective. These curves also illustrate the previously noted meager 

 improvement for weak speech which accompanies the increase from f^ = 

 100 to 1,000 when B = 100. Actually, an optimum solution is attained 

 for an intermediate value of ^l, but the advantage is too small to be of 

 interest (see Figs. 10 to 13). 



o 



UJ 



a 



10 20 40 60 100 200 400 600 1000 



C 



Fig. 17 — Signal to quantizing error power ratios (in db) as a function of rela- 

 tive signal power for companding corresponding to n = 500. Symbols have the 

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



