INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 689 



single compressor)^' ^ sufficiently to guarantee exact coincidence of the 

 average input signal (e = 0) in each channel and the center of the — V 

 to -\-V voltage range {e = 0) presented by the compressor. Thus the 

 input, e, would appear to the compressor in the form E = e -{- Cq . The 

 consequences of the appearance of the undesirable constant term, eo , 

 may be inferred from study of Figs. 10 to 13 and (80). 



We shall assume that, owing to the present state of gating technology, 

 B = V/co may reasonably be expected to assume values in the range 

 100 < 5 ^ 1,000. 



For companding corresponding to 100 ;S m^ 1,000, Figs. 10 to 13 

 indicate that, if B can be confined to the vicinity of 1,000, the departure 

 from the ideal behavior corresponding to B = qo will be virtually negli- 

 gible. 



However, should it prove necessary to work with B = 100, it is clear 

 from Figs. 10 to 13 that the companding improvement for weak signals 

 would be relatively independent of ju in the inter\'al 100 ;S M ^ 1,000 

 (with a saturation value of about 20.5-22.5 db).* In this event, compres- 

 sion to a degree greater than that represented by fj. = 100 would provide 

 less improvement for strong and average speech without the compensa- 

 tion of significantly greater improvement for weak signals. Reduction 

 of M below 100 would not be fruitful since the sensitivity of companding 

 improvement to changes in n is restored for values satisfying the condi- 

 tion of (fi/B) = (m/100) < 1. 



The significance of the values eo '^ F/1,000 and TVlOO n^ay perhaps 

 better be appreciated in terms of a comparison of eo with the weakest 

 signals under consideration. Since (B/C) = \/^/eo , a signal to dc bias 

 power ratio may be calculated, in db, from the expression 20 logio 

 {B/C). For the weakest signals under consideration (C '~ 400), the 

 values B = 1,000 and 100 correspond respectively to (v^/<'o) = 2.5 

 and 0.25, or to signal to dc bias power ratios of +8 db and —12 db. 

 Thus, for the hypothetical system now under study, the value of Co 

 becomes significant (roughly) when it exceeds the weakest rms signal. 



Actually eo would be expected to vary with time for a given channel 

 and to vary from channel to channel at any instant. On the assumption 

 that I eo I = F/lOO (i.e., B = 100) will constitute the upper bound of 

 such variations, the companding impro^'ement corresponding to a 

 particular value of n must now be specified in terms of the region between 

 the B = 'x> and B = 100 curves in Figs. 10 to 13, i-ather than by refer- 

 ence to a single value of B and its corresponding cuixc. Since the lower 



* This corre.spoiid8 to tlie beliavior of D^ for (fi/B) » 1 which was noted in the 

 discussion of (30). In this connection, see the discussion of Fig. 19. 



