Wigner-space synthesis of discrete-time periodic signals

A procedure that facilitates at least-squares synthesis of periodic, discrete-time signals from Wigner quasi-distributions is proposed. The scheme is based on expanding the desired time sequence on a generally nonorthogonal, Gabor-type basis whose associated biorthogonal function presumably exists. The specific basis selection may crucially affect the efficiency and quality of the ensuing synthesis procedure. The cited basis type constitutes a considerable generalization over the standardly used orthogonal variety, thus creating previously unavailable degrees of freedom. Of primary significance is the acquired capability of generating time-frequency basis functions that are well localized. Localization is a highly desirable property that can advantageously serve in various applications. It is shown and numerically demonstrated that benefits of localization as well as the fact that achieving effective time-frequency basis localization renders a certain degree of oversampling unavoidable