Marching and spatial-spectral filtering of localized phase-space representations of wave fields in layered media

Abstract

Spatial and spectral (directional) information of the wave data are of equal importance in the analysis and synthesis of wave phenomena. Their simultaneous collaboration in a phase-space format may be achieved by incorporating windowing techniques into (conventional) spectral integrals. The result is a local-spectral representation of the field that is concentrated inherently around physically meaningful regions in phase space. This representation is most naturally suited to perform simultaneous spatial and spectral processing of wave data and therefore may serve as a powerful tool in a variety of applications such as remote sensing, imaging, field reconstruction, and more. In this work a method to propagate the local spectra of wave fields through plane stratified media is developed and discussed. An adaptive marching algorithm that permits control of the localization process will be presented. The ability of the new scheme to perform simultaneous spatial and spectral data filtering of wave phenomena, and its resolving power in phase space, will be discussed and demonstrated by means of numerical examples.