New time-frequency representations: higher order warped Wigner distributions

We propose a new higher order time-frequency representation (TFR), the higher order generalized warped Wigner distribution (HOG-WD), by warping the higher order Wigner distribution. The HOG-WD is important for analyzing signals with dispersive instantaneous frequency characteristics. In this paper, we (i) provide a HOG-WD formulation, (ii) give important special cases of the HOG-WD based on different warpings, (iii) discuss alternative HOG-WD formulations in terms of a 1-D generalized transform and in terms of a generalized higher order ambiguity function, (iv) discuss some desirable properties of the HOG-WD, and (v) define a higher order, generalized (alternating sign) frequency-shift covariant class of TFRs based upon smoothed versions of the HOG-WD.