When is instantaneous frequency the average frequency at each time?

The interpretation of instantaneous frequency has been a subject of interes t for many Sears, One interpretation is that it is the average frequency at each time in the signal. We prove that instantaneous frequency equals the average frequency at each time only when there is symmetry in the instantan eous spectrum, as recent empirical evidence has suggested. Also, when there is such symmetry, the average frequency at each time equals the median fre quency at each time.