Wigner distributions (nearly) everywhere: time-frequency analysis of signals, systems, random processes, signal spaces, and frames

Authors:
Gerald Matz;Franz Hlawatsch
Affiliations:
Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Gusshausstrasse 25/389, A-1040 Wien, Austria;Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Gusshausstrasse 25/389, A-1040 Wien, Austria
Venue:
Signal Processing - From signal processing theory to implementation
Year:
2003

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Abstract

The Wigner distribution (WD) is perhaps the most prominent quadratic time-frequency signal representation. In this paper, which has mainly tutorial character but also contains some new results, we describe extensions of the WD concept to multidimensional vector signals, nonstationary random processes, linear time-varying systems (deterministic and random), linear signal spaces, and frames. We discuss the interpretation and properties of these WD extensions and various relations connecting them. Some application examples are also provided.