Virtues and vices of quartic time-frequency distributions

We present results concerning three different types of quartic (fourth order) time-frequency distributions (TFDs). First, we present new results on the previously introduced local ambiguity function and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. Second, we introduce the class of quartic, shift-covariant, time-frequency distributions and investigate distributions that localize quadratic chirps. Finally, we present a shift covariant distribution of time and chirp rate