INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



685 



perturbation, we wish to study the modification of companding improve- 

 ment produced by the introduction of a finite value oi B = V/eo , i.e., 

 .substitution of (30) for (27), when A'', V, C, A, and fx, remain unchanged. 

 In Figs. 10 to 13 we have replotted the companding improvement 

 curves shown in Fig. 8 for ^ = 100, 200, 500, and 1,000, respectively. 

 These curves correspond to -B = oo . The difference between these curves 

 and those for finite values of B in Figs. 10 to 13 is the impairment (in db) 

 inflicted by the presence of eo . This impairment may be appreciable for 

 weak signals (large C). As already noted in connection with (32) the im- 

 pairment is not severe for (n/B) <3C 1. Furthermore, the appropriation 

 of the algebraic role of n by B, when B « ju, which was previously noted 

 in (32), manifests itself in the striking similarity of the weak signal be- 

 havior of all the curves for B = 50 and 100 in Figs. 10 to 13. 



8 10 20 40 60 100 



c 



200 



400 600 1000 



Fig. 12 — The effect of a "do component" on companding improvement for 

 M = 500. For further details, see the caption of Fig. 10. 



