STEADY STATE DELAY AND APERIODIC SIGNALS 231 



The delay, 



PI _ rp _ rp _ Bi -\- ksi r 



While there is a superficial similarity between this and the phase delay (1), 

 it is of little real significance; w, in (1), is determined by the aggregate 

 increase in phase shift with frequency, while k, is determined mainly by the 

 rate of increase at w\ . An example of a situation in which the two delays 

 are very different, is furnished by a wave guide when the frequency only 

 just exceeds the cutoff. The phase delay is then almost zero while the rate 

 of change of phase shift with frequency is very large. 



Thus the delay based on maximum absolute value depends on both the 

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

 delay. There remains to examine this dependence in more detail. The 

 value of kz depends on the spectrum of the signal as well as the characteristic 

 of the system. It is of interest to see if it can be replaced by a quantity 

 derived from the system characteristic alone. The most obvious thing to 

 try is a delay which is derived from the phase shift of the system in the 

 same w-ay that the time of absolute maximum is derived from that of the 

 signal spectrum. This would be 



r, _ -Si + hiT 

 Us — , 



where 



The difference between this and the aperiodic delay based on absolute 

 value is 



COl 



= — (^0 + ^2 — ^3). 

 COl 



Since ki — ks is either zero or an integer and | '^s 1 is less than - , if 



- 2 < ^0 + ^2 < 2 > 

 Ds - Da = 0. 



