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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



with v{ — e) = —v{e) as usual. The "m-characteristics" specified by 

 (A-7) are to be compared with the "^-characteristics" specified by (8). 

 From the derivation of (A-6) it is known that optimum companding 

 will be produced when m is given by the critical value, 



rric = \/2C/3 

 This is the analogue of (36) defining jXc for the ju-ensemble. 



(A-8) 



3. Properties of the ''m- Ensemble^' 



We shall now interpret the properties of the /n-ensemble of compan- 

 dors, for which the ensemble improvement limit (m = nic) actually 



1.0 



0.9 



0.7 



0.6 



> 



> 



0.5 



0.4 



0.3 



0.2 



0.1 







\ 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



(e/vj 



Fig. 21 — Typical m-ensemble compression characteristics determined by 

 equation (A-7). Note the strong emphasis on weak signal amplitudes. These 

 curves may be compared with those for the ^u-ensemble in Fig. 3. 



