Generalized ambiguity functions and wavelets

Abstract

Summary form only given, as follows. A class of linear operators on L2(R2) are introduced that, when acting on rank-one tensors, yield ambiguity functions and their generalizations. Many properties of ambiguity functions become transparent in this setting. The L2-synthesis problem by functions in the range of these operators is solved. The same approach applied to functions whose Fourier transforms are rank-one tensors yields analogous results for wideband ambiguity functions (wavelet transforms).