On Estimating the Instantaneous Frequency of a Gaussian Random Signal by Use of the Wigner-Ville Distribution

In this correspondence, the form of the one-dimensional probability distribution function for the Wigner-Ville, or evolutive spectrum, and the instantaneous frequency of a Gaussian random process is derived by use of an orthogonal decomposition of the process covariance matrix. No narrow-band assumptions are made. Natural estimators for the evolute spectrum and the instantaneous frequency are defined, and the form of the distribution functions are derived. The properties of these estimators are examined with particular reference to the effects of windowing operations used in the calculation. The usefulness of the results is indicated, and examples are presented