INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 



683 



The abscissa has been furnished with an additional scale, based on 

 (3-i), showing the signal power in db below that of a full load sine wave. 

 Thus the curves in Fig. 8 embody the information recjuired for the choice 

 of a compandor characteristic in a form which is suitable for practical 

 applications. It is clear that the effect of companding varies considerably 

 with the volume of the signal and that strong signals are actually im- 

 paired. For each value of n, there is a value of C (in the weak signal, or 

 large C range) beyond which the db improvement is essentially independ- 

 ent of C. The threshold value of C corresponding to such saturation in- 

 creases ^^^th increasing /x. This saturated improvement for weak signals 

 reflects the linearity of compression for (e/V) <K m~^- In this region, uni- 

 form (juantization prevails so that the ratio of the uniform step sizes 

 before and after companding (given by the linear amplification factor) 

 may be used to deduce a constant companding improvement for the 



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UJ 



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 tr 



Q. 



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Q 



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Q. 



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28 

 26 

 24 

 22 

 20 

 18 

 16 

 14 

 12 

 10 



SIGNAL POWER 

 5 1CT 15 



IN DECIBELS BELOW FULL LOAD SINUSOID 



20 25 30 35 40 45 50 



6 8 10 



20 40 60 100 



C 



200 



400 600 100C 



Fig. 10 — Modification of companding improvement, for /n = 100, resulting from 

 the shift of the (luiescent value of the signal by an amount fn from the center of the 

 quantized voltage range (see Fig. 1). The relative size of the "dc component" is 

 given i>y the jiarameter B = V |e^^ as defined in equation (211). The algebraic usurpa- 

 tion of the role of /x by B, for B « tx, results in the striking similarity of the weak 

 signal behavior of the curves for 5 = 50 and 100 in Figs. 10 to 13. 



