Moment densities of propagating wave fields

Abstract

Matrix elements of formal differential operators for time and frequency are used to derive local centred conditional moments, or moment densities, for some representative propagating wave fields. The moment densities for one dynamical phase space variable are given as functions of its Fourier conjugate variable and other parameters, and are constrained and defined only by the signal used to compute them. The information thus consistently gained is the phase space track of the signal; its instantaneous frequency and group delay, dispersion about those local mean values, and higher order shape parameters for the distribution of each dynamical variable such as skew and kurtosis. Moment densities for laser pulses, acoustic resonances, and solitons are examined.