Third-order Wigner distributions: definitions and properties

Gerr´s Wigner bispectrum is generalized, and the properties of the resulting time-frequency distribution are studied. Continuous- and discrete-time versions, aliasing problems, and analysis and synthesis techniques are studied. Extensions to higher-order Wigner distributions are briefly discussed. It is stressed that third-order Wigner distributions will enjoy the robustness of third-moment statistics to symmetrically distributed noise only if they are average across time (short-time bispectra) or across independent realizations. Potential applications are discussed, including detection and quantification of quadratic phase coupling in nonstationary signals, such as speech and seismic signals, as well as electroencephalograms and electrocardiograms