708 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



(/) Illustrative Application 



Consider the possibility of choosing a member of the m-ensemble for 

 application to the hypothetical PCM system already discussed in con- 

 nection with the /i-ensemble. It will be recalled (see Figs. 15-18) that 

 we were able to choose degrees of logarithmic compression which would 

 yield signal to quantizing error power ratios in excess of about 20 db for 

 all volumes (4.5 S C ^ 450) by using as few as six or seven (depending 

 on the choice of /x) digits per code group. In contrast, Fig. 26 reveals 

 that no value of m will meet this requirement since the curves fall so 

 rapidly on either side of the sharp maxima. In short, the members of 

 the m-ensemble are each too specialized for successful application to 

 such a broad volume range. 



Further detailed comparison between the numerical results for the 

 two ensembles seems inappropriate, since it is not at all clear that the 

 inequitable treatment of the various samples in a given signal by mem- 

 bers of the m-ensemble (see Fig. 23) permits an adequate description of 

 signal quality solely in terms of quantizing error power. Under these cir- 

 cumstances, subjective effects beyond the scope of the present analysis 

 might assume a dominant role. 



REFERENCES 



1. H. S. Black, Modulation Theory, Van Nostrand, N. Y., 1953. 



2. W. R. Bennett, Spectra of Quantized Signals, B. S.T.J. , 27, pp. 446-472, 



July, 1948. 



3. Oliver, Pierce and Shannon, The Philosophy of PCM, Proc. I.R.E., 36, pp. 



1324-1331, Nov., 1948. 



4. Clavier, Panter and Dite, Signal-to-Noise-Ratio Improvement in a PCM 



System, Proc. I.R.E., 37, pp. 355-359, April, 1949. 



5. P. F. Panter and W. Dite, Quantization Distortion in Pulse-Count Modulation 



with Nonuniform Spacing of Levels, Proc. I.R.E., 39, pp. 44-48, Jan., 1951. 



6. L. A. Meacham and E. Peterson, An Experimental Multichannel Pulse Code 



Modulation System of Toll Quality, B.S.T.J., 27, pp. 1-43, Jan., 1948. 



7. H. S. Black and J. O. Edson, Pulse Code Modulation, Trans. A.I.E.E., 66, 



pp. 895-899, 1947. 



8. Clavier, Panter and Grieg, Distortion in a Pulse Count Modulation Sj'^stem. 



Elec. Eng., 66, pp. 1110-1122, 1947. 



9. J. P. Schouten and H. W. F. Van' T. Groenewout, Analysis of Distortion in 



Pulse Code Modulation Systems, Applied Scientific Research, 2B, pp. 277- 

 290, 1952. 



10. W. M. Goodall, Telephony by Pulse Code Modulation, B.S.T.J., 26, pp. 395- 



409, July, 1947. 



11. C. B. Feldman and W. R. Bennett, Bandwidth and Transmission Performance, 



B.S.T.J., 28, pp. 490-595, July, 1949. 



12. W. R. Bennett, Sources and Properties of Electrical Noise, Elec. Eng., 73, pp. 



1001-1008, Nov., 1954. 



13. C. Villars, Etude sur la Modulation par Impulsions Codies, Bulletin Tech- 



nique PTT, pp. 449-472, 1954. 



14. J. Boisvieux, Le Multiplex a 16 Voies h Modulation Codde de la C.F.T.H., 



L'Onde Electrique, 34, pp. 363-371, Apr., 1954. 



