Two-Dimensional Convolutions, Correlations, and Fourier Transforms ofCombinations of Wigner Distribution Functions and Complex Ambiguity Functions

摘要

A number of new two-dimensional Fourier transforms of combinations of crossWigner distribution functions, W, of convolution form or correlation form are derived. In addition, similar relations are obtained for combinations of cross complex ambiguity functions, X. Their great generality subsumes most of the already known available properties, such as: the volume constraint of magnitude-squared ambiguity functions; the positivity of the convolution of two Wigner distribution functions; and Moyal's theorem. Keywords: Two-dimensional, Convolution, Correlation, Temporal correlation, Wigner distribution, Ambiguity function, Fourier transform, Spectral correlation. (Author) (KR)