INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



C69 



10" 



> 



> 



10" 



10" 



10" 



^ %0-2 



(e/v) 



10" 



6 8 



Fig. 4 — Logarithmic replot of compression curves shown in Fig. 3, to indicate 

 detailed behavior for weak samples. The characteristic employed in the experi- 

 ments of Meacham and Peterson" (M & P) is also shown. Similarity between this 

 characteristic and the ^ = 100 curve testifies to the probable realizability of these 

 logarithmic characteristics. 



from consideration of the ratio of step size to corresponding pulse ampli- 

 tude, (A^/f'), since this quantity is a measin-e of the maximum fractional 

 quantizing error imposed on individual samples. Hence the relation, 



(e/Ae) = [iV/2 log (1 + m)](1 + F/zxe)"' 



[which follows from (12a)] has been plotted, for /n = 10, 100, and 1000, 

 in Fig. 5. These curves reflect the fact that the sample to step size ratio 

 reduces to the asymptotic forms: 



{e/^e) -> Ar/2 log (1 + /x) = const for (e/F) » m~^ 



and 



(e/Ae) -> [iV/2 log (1 + \j)\{ixe/Y) for (e/7) « m"' 



