Steady State Delay as Related to Aperiodic Signals

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 delay. When it is the time of maximum absolute value, the delay depends on the signal spectrum, 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.