New higher order spectra and time-frequency representations for dispersive signal analysis

For an analysis of signals with arbitrary dispersive phase laws, we extend the concept of higher order moment functions and define their associated higher order spectra. We propose a new higher order time-frequency representation (TFR), the higher order generalized warped Wigner distribution (HOG-WD). The HOG-WD is obtained by warping the previously proposed higher order Wigner distribution, and is important for analyzing signals with arbitrary time-dependent instantaneous frequency. We discuss links to prior higher order techniques and investigate properties of the HOG-WD. We extend the HOG-WD to a class of higher order, alternating sign, frequency-shift covariant TFRs. Finally, we demonstrate the advantage of using the generalized higher order spectra to detect phase coupled signals with dispersive instantaneous frequency characteristics.