500 



BELL SYSTEM TECHNICAL JOURNAL 



6 the minimum slopes are zero hence no delay can be subtracted which 

 applies to the signal as a whole. '^ 



In order to observe the effects of phase distortion in some simple 

 cases ^2 we shall show oscillographs of some sent and received non- 

 periodic waves. These waves are of the type that are zero up to time 

 / = 0, take the form y sin (wo^ + Q) between / = and / = T and are 

 zero for all future time.^^ A Fourier Integral analysis of these waves 

 would show they contained energy over the entire frequency range, 

 though most of it is confined to frequencies in the neighborhood of /o 

 where /o = ooq/Itt. 



79,200 



72,000 



0.220 



800 1200 1,600 2,000 



frequency' in cycles per second 



2.400 



2.800 



Fig. 7 — Insertion phase and delay characteristics of a 600 mile length of medium 



heavy loaded cable (including repeaters). 



Such waves as these are elementary waves which can readily be 

 produced in the laboratory and the effects of distortion on them ob- 

 served or in special cases the effect may be calculated. 



" This assumes of course that energy falls in the frequency range where the slope 

 approximates zero. If such were not the case for a particular signal a definite delay 

 could be ascribed given by the minimum slope in the range where the frequency com- 

 ponents of consequence fall. 



1- The effect of phase distortion on speech and music signals is discussed in the 

 paper by J. C. Steinberg already mentioned. 



'2 It is of interest to note that any complex wave which is zero at all times prior to 

 / = and also at all times after t = T may be regarded as the sum of such finite 

 components as these. Analyze it by means of Fouriers Series as though it repeated it- 

 self as a steady state wave for all time. Then multiply all of the steady state sinusoidal 

 components by zero for all time prior to / = and after t = T retaining only the por- 

 tion for the interval of time T. The resultant simple components will add up to giv-e 

 the original complex wave. After distortion the distorted components will add up 

 to give the distorted wave as a whole. 



