1010 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



less than 10"^ nepers and radians respectively. This would correspond to 

 an rms gain deviation over the transmission band well below 0.08 db 

 and an rms deviation from a linear phase characteristic well below 0.6 

 degrees. Since these tolerances are difficult to realize in actual systems, 

 at least for wire circuits, characteristic distortion rather than noise may 

 impose a limitation on channel capacity of systems employing about the 

 same bandwidth as the original signal. 



In accordance with (16.01), the bandwidth can in principle be halved 

 without change in channel capacity if the signal-to-noise ratio is squared, 

 i.e., if N/P = 10"^ rather than 10~* in the previous example. The toler- 

 able rms amplitude and phase deviations would then be 



^ + ^ « 10~^ 



Thus both a and h would have to be substantially smaller than about 

 10"*, which would preclude a substantial bandwidth saving in practical 

 systems from the standpoint of characteristic distortion, even if it were 

 feasible from the standpoint of signal power required to override noise. 

 The above considerations apply when faithful reproduction of the 

 transmitted signal is required, as for example in data transmission. In 

 speech transmission considerable distortion can be tolerated, a circum- 

 stance which permits appreciable phase distortion in the usual frequency 

 division system without noticeable impairment of intelligibility, but 

 which cannot be taken advantage of in time division pulse systems be- 

 cause of the resultant intersjonbol interference. The characteristics of 

 speech sounds also permit a reduction in the bandwidth of the original 

 transmitted signal, by such devices as vocoders or frequency compandors, 

 without excessive impairment of intelligibility. 



ACKNOWLEDGMENTS 



This paper is based on studies in connection with the application of 

 pulse systems to ware circuits, suggested by M. L. Almquist and J. T. 

 DLxon and carried out under their direction. Some of these studies were 

 made on behalf of the Signal Corps, under contract W-36-039-SC-38115. 

 The Signal Corps Engineering Laboratories have consented to the pub- 

 Hcation of results obtained in these studies. The writer had the benefit 

 in these studies of discussions with C. B. Feldman and W. R. Bennett, 

 and of some of their memoranda on pulse modulation systems. He is also 

 thankful for comments and advice from F. B. Llewellyn and others in 

 connection with preparation of the paper. 



REFERENCES 



See Part I. 



