An analysis of instantaneous frequency representation using time-frequency distributions-generalized Wigner distribution

This paper presents an analysis of the representation of instantaneous frequency using time-frequency distributions of energy density domain. Similarity to the ”ideal” instantaneous frequency presentation is chosen as a criterion for comparison of various distributions. Although all the commonly used distributions suffer from the artifacts along frequency axis, it is shown that the Wigner distribution is the best among them, with respect to this criterion. The generalization of Wigner distribution LWD is introduced to decrease the artifacts. The properties of the LWD are analyzed. It is shown that, at the expense of an insignificant increase in computation time, much better results are obtained. The theory is illustrated by a numerical example with the frequency modulated signals.