Generalized Representation of Phase Derivatives for Regular Signals

This paper introduces a new generalized complex-lag moment which produces joint time-“phase derivatives” distributions. For the choice of the time-“first-order phase derivative,” which stands for time–frequency representation, this distribution can be seen as a form of the Wigner–Ville distribution. Moreover, this generalization leads to distributions with highly reduced inner interferences caused by the nonlinearity of the signal's phase. It can also be seen as a polynomial distribution since the $N$th-order distribution produces no inner interferences for polynomial phase law of order $N$ . Implementation of these distributions is addressed. The results are illustrated by examples.