Physical wavelets and radar: A variational approach to remote sensing

Physical wavelets are acoustic or electromagnetic waves, resulting from the emission of a time signal by a localized acoustic or electromagnetic source moving along an arbitrary trajectory in space. Thus, they are localized solutions of the wave equation or Maxwell's equations. Under suitable conditions, such wavelets can be used as ''basis'' functions, to construct general acoustic or electromagnetic waves. This gives a local alternative to the construction of such waves in terms of (nonlocal) plane waves, via Fourier transforms. In this tutorial paper, we give a brief, self-contained introduction to physical wavelets, and apply them to remote sensing. We define the ambiguity functional, a generalization of the radar and sonar ambiguity functions, which applies not only to wideband signals, but also to targets and radar platforms executing arbitrary nonlinear motions.