INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 687 



the value of 10 db is probably no more than a few db removed from the 

 value which would be chosen in any efficient application of PCM to 

 quality telephon3^ It results from the need to balance the requirement 

 of a value of T' sufficiently high to avoid intolerable clipping of the peaks 

 of the loudest signals against the obvious ad\'antage of reducing the 

 quantizing step size by minimizing the voltage range to be ciuantized. 

 We have neglected clipping in our calculations since it was assumed that 

 the significant peaks of the loudest signals should not exceed T^ for qual- 

 ity telephony. Existing information on clipped speech" " and one digit 

 PCM^" indicates that the clipping impairment we seek to avoid is largely 

 one of loss of naturalness rather than reduction in intelligibility. The 

 choice of a maximum volume 10 db below a sinusoid of amplitude T" 

 implies that speech peaks 13 db, [see (34)], above the maximum rms 

 signal voltage are being ignored, which appears reasonable in the light 

 of available experimental evidence. ' 



It follows from these assumptions that the average and weakest 

 signals are respectively 30 db and 50 db below full sinusoidal modula- 

 tion. 



B. Choice of Compression Characteristic 



1 . Ideal Behavior for Speech 



If we adopt the aim of achieving the smallest over-all departure from 

 the ensemble limit of improvement, it seems reasonable to choose that 

 compandor in the optimum ensemble which corresponds to average 

 speech (C = 45). This requirement, in conjunction with Fig. 7, estab- 

 lishes a lower bound of about 150 for /n. The significance of this choice 

 may be clarified by reference to Fig. 14, which depicts departures from 

 the optimum ensemble limit of improvement, resulting from restriction 

 to a single value of m for all volumes. 



The corresponding upper bound will be determined by the alternative 

 of furnishing optimum improvement to the weakest signals (C = 450) 

 in spite of the concomitant impairment of loud speech. Reference to 

 Fig. 7 then dictates a choice of ^ in the vicinity of 2,500. From Fig. 6 

 it is clear that this value implies that D is essentially constant and in- 

 dependent of C throughout the range of interest. Appreciably larger 

 values of n would actually lead to the undesirable extreme oi D > 

 ^M-Mix for all signals under consideration. 



We therefore conclude that attention may profitably be confined to 

 the interval 150 ^ m ,^ 2,500, the magnitude of which is adequately 

 conveyed by the simple expression 



100 ^ M ;^ 1,000 (38) 



