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.