Steady State Delay as Related to Aperiodic Signals 



By R. V. L. HARTLEY 



The concepts of phase and envelope delay, as applied to any linear 

 system, rather than only to a medium, are discussed. Criteria are set 

 up for the time of occurrence of that part of an aperiodic signal which 

 corresponds to a small segment of the spectrum. The original spectrum 

 of the signal gives the time of entry and this spectrum as modified by the 

 phase characteristic of the system gives the time of exit. 



If the amplitude is constant over the segment, it is shown that when 

 the criterion is the time of maximum envelope of the disturbance, the 

 aperiodic delay is identical with the envelope delav. When it is the 

 time of maximum absolute value, the delay depends on the signal spec- 

 trum, the phase shift of the system, and the envelope delay, but not on 

 the phase delay. 



If the amplitude vaies rapidly with frequency, the component of an 

 aperiodic disturbance which corresponds to a narrow segment of the 

 spectrum persists so long that the resulting over-lapping of neighboring 

 segments makes their interpretation difficult. 



TN the earlier applications of steady state theory to transmission prob- 

 -*- lems the emphasis was placed on the variation of amplitude with fre- 

 quency. The use of long loaded lines made it necessary to take account 

 of phase distortion^ as well. With the development of telephotography and 

 television^, the phase characteristic was found to provide a useful index for 

 predicting the overlapping of adjacent picture elements. For these purposes 

 it has been found convenient to express the phase characteristic in terms of 

 phase or envelope delay. These may be called "steady state delays" since 

 they are defined and measured in terms of sinusoidal disturbances of ad- 

 justable frequency. However, the signals for which they are intended to 

 furnish an index are aperiodic in nature. It seemed worthwhile, therefore, 

 to examine more closely the relations existing between "aperiodic delays," 

 defined in terms of such signals, and steady state delays. 



Let us first review the development of the concepts of steady state delay. 

 Early in the study of the propagation of sinusoidal waves a distinction was 

 made between phase and group velocity. If we fix on a particular distance 

 of transmission the ratio of this distance to each of these two velocities 

 may be interpreted as a delay associated with the transmission. In the 



* For discussion and references see "Phase Distortion and Phase Distortion Correc- 

 tion," S. P. Mead, B. S. T. J., Vol. VII, p. 195, 1928. 

 ^ Symposium on Television, B. S. T. J., Vol. VI, p. 551. 



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