Instantaneous frequency computation: theory and practice

Matthew J. Yedlin, Gary F. Margrave, Yochai Ben Horin

We present a review of the classical concept of instantaneous frequency, obtained by differentiating the instantaneous phase and also show how the instantaneous frequency can be computed as the first frequency moment of the Gabor or Stockwell transform power spectrum. Sample calculations are presented for a chirp, two sine waves, a geostationary reflectivity trace and a very large quarry blast. The results obtained clearly demonstrate the failure of the classical instantaneous frequency computation via differentiation of the instantaneous phase, the necessity to use smoothing and the advantage of the first moment computation which always results in a positive instantaneous frequency as a function of time. This research points to the necessity of devising an objective means to obtain optimal smoothing parameters. Future work will focus on using linear and nonlinear inverse theory to achieve this goal.