INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



681 



^- 



z 



lU 



> 



o 

 ct 



a. 



J 



z 



Q 

 Z 

 < 



a. 



5 



J 



30 

 28 

 26 

 24 

 22 

 20 

 18 

 16 

 14 

 1 2 

 10 



SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 

 5 10 15 20 25 30 35 40 45 50 



6 8 10 



20 40 60 100 



C 



200 



400 600 1000 



Fig. 8 — Companding improvement (in db), as calculated from equation (37), 

 for various values of ix. The saturated improvement for weak signals (relativel}' 

 constant ordinate for large C values) is identical with the asj'mptotic behavior 

 for weak signals which is predicted by Fig. 9. 



is tangent to this lower bound at the single value of C which corresponds 



to /X = /ic • 



In conventional systems, a single common channel compandor, char- 

 acterized by a single value of ju, is substituted for the optimum ensemble. 

 Although Z)^_MiN is then attainable at only one value of C, it is instruc- 

 tive to compare each value of D with the corresponding value of Z)^_min. 

 Indeed, consideration of the optimum ensemble has, in one sense, reduced 

 the problem of choosing an appropriate /x for a given application to the 

 choice of that particular value of C at which eciuality of D and /);i_min 

 is desired. 



In Fig. 6, the line representing performance in the absence of compand- 

 ing corresponds to (33) for Do . Do and D^_min are seen to be similar for 

 strong signals (low values of C). Furthermore, it is important to note 

 that Do does not constitute an upper bound for D; thus the companding 



