A GENERALIZATION OF THE GABOR-HELSTROM TRANSFORM.

Abstract : A new class of integral transforms which generalizes Helstrom's integral expansion of a signal is developed. The forward transform of the signal, obtained by a one dimensional integration, is a representation of the signal in both time and frequency. All transforms of this class are what is defined as a generalized cross-ambiguity function. Necessary and sufficient conditions for a function of two variables to be a generalized cross-ambiguity function are given. The inverse transform is a two dimensional integral over time and frequency. A new method of synthesizing an ambiguity function is demonstrated. The cross-ambiguity function of the unknown signal and a chosen known signal is first obtained, and from this, the unknown signal is obtained by the factorization theorem for cross-ambiguity functions. (Author)