On the normalized hilbert transform and its applications in remote sensing

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 been often noted, natural physical processes are mostly nonlinear and nonstationary. Yet, there have historically been very few options in the available analysis methods to examine data from such nonlinear and nonstationary processes. The available methods have usually been for either linear but nonstationary, or nonlinear but stationary, and statistically deterministic processes. The need to examine data from nonlinear, nonstationary, and stochastic processes in the natural world is due to the nonlinear processes which require special treatment. The past approach of imposing a linear structure (by assumptions) on the nonlinear system is 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.