INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



707 



(c) Signal to Quantizing Error Power Ratios 



The curves in Fig. 26 are drawn for the representative case oi N = 

 2^ = 128 quantizing steps (7 digit PCM). The corresponding ensemble 

 limit is constant, as might be expected from (A-4), except for strong 

 signals where the effects of peak clipping become noticeable. 



In the region where this ensemble limit is constant, departures from 

 the improvement limit resulting from the use of a single value of m for 

 all volumes may be read directly from the ordinates shown at the right 

 in Fig. 26. In comparing these departures from maximum improvement 

 with the analogous ^-ensemble curves in Fig. 14, it must always be 

 recalled that, in view of its role in the solution of the variational problem, 

 the m-ensemble limit represents the actual minimum quantizing error 

 power consistent with the probability density specified by (A-5). 



SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINOSOID 

 5 10 15 20 25 30 35 40 45 50 



Fig. 26 — Signal to quantizing error power ratios as a function of relative signal 

 power for 7 digits and various ^/-compandors. The curves may he compared with 

 those for 7 digits in Figs. 15 to 18. The auxiliary ordinates at the right of the pres- 

 ent figure ai)ply for C >, 10, where the ///-ensemble limit is effectively constant; 

 departures from this limit, resulting from the use of a single value of vi for all 

 volumes, may be read directly from this scale, for comijarison with Fig. 14. The 

 latter comparison illustrates the narrow volume limitation of the members of the 

 '/i-ensemble. 



