An approach to the polynomial Wigner distributions

The distribution concentration along the instantaneous frequency is one of the interesting research topics in time frequency analysis. The oldest and simplest transform for time-frequency signal representation is the short-time Fourier transform (STFT). However, it may achieve high concentration at the instantaneous frequency only for signals whose frequency is constant. The quality of the time-frequency signal representation may be improved using the Wigner distribution. An analysis of the polynomial Wigner distributions, with respect to the concentration in the time-frequency plane is presented. A distribution with "complex-time" argument is defined. The concentration of the polynomial and the "complex-time" distributions is illustrated by examples.