ABSTRACT
The development of this new approach was motivated by the need to describe nonlinear distorted waves in detail, along with the variations of these signals that occur naturally in nonstationary processes (e.g., ocean waves). As has often been noted, natural physical processes are mostly nonlinear and nonstationary. Yet, historically there have been very few options in the available analysis methods to examine such data from nonlinear and nonstationary processes. The available methods have usually been either for linear, but nonstationary, or nonlinear, but stationary, and statistically deterministic processes. There is a need to examine data from nonlinear, nonstationary, and stochastic processes in the natural world, and this requires special treatment. The past approach of imposing a linear structure (by assumptions) on the nonlinear system is just not adequate. Other than periodicity, the detailed dynamics in the processes from the data also need to be determined. This is needed because one of the typical characteristics of nonlinear processes is its intrawave frequency modulation (FM), which indicates the instantaneous frequency (IF) changes within one oscillation cycle.
