INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



691 



36 



<n 34 

 ai 



LU 

 Q 



-, 30 



a. 



ct 



LU 



5 



o 



Q. 



a. 

 o 

 cc 

 a 



OJ 



u 



z 



N 



I- 



z 

 < 



a 



26 



24 



22 



20 



18 



16 



14 



< 



Z 



in 



12 



10 



SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 

 5 10 15 20 25 30 35 40 45 50 



8 10 



20 



40 60 



100 



200 



400 600 1000 



Fig. 15 — Signal to quantizing error power ratios (calculated, in db, from equa- 

 tion (39)) as a function of relative signal power for companding corresponding to 

 n = 100. Curves are shown for n = 5,6, and 7 digits per code group. For compari- 

 son, the results for seven digits in the absence of companding {/j, = 0) as well as 

 for the ensemble upper limit (fj, = fie) are included. B = x, throughout. 



steps, it is apparent that the upper Hmit of companding improvement 

 will set a lower limit on the number of digits required for satisfactory 

 operation. 



Once again we begin with the consideration of pure speech signals. 

 The expression 



-10 login (7)') = -20 logic 7) 



Signal to Quantizing Error PoAver Ratio in db 



(39) 



has been plotted against (' in Figs. 15 to 18 for n = 100, 200, 500, and 

 1,000 respectively. In each case the behavior for 5, (i, and 7 digits is 

 compared with the extremes of m = (no companding) and m = Mc 

 (ensemble upper limit) for 7 digits. 



It must be conceded at the outset that experimental work is required 

 to formulate standards for quantizing error power similar to those 



