Time-frequency distributions with complex argument

A distribution highly concentrated along the group delay or the instantaneous frequency (IF) is presented. It has been defined by introducing a signal with a complex argument in time-frequency (TF) analysis. Realization of a signal with a complex argument, using a signal with a real argument, is described. The reduced interference realization of the complex argument distribution, in the case of multicomponent signals, is presented. The proposed distribution is used for the IF estimation. It is shown that the estimation can be improved with respect to the Wigner distribution based one since the bias can be significantly reduced with only a slight increase of the variance. The theory is illustrated by examples.