Double-dimensional distributions: another approach to "quartic" distributions

We present the definitions of double-dimensional time-frequency distributions, especially the Wigner distribution (WD) of the WD and the ambiguity function of the ambiguity function. The first coincides with the notion of the local ambiguity function presented in the papers of O'Neill and Williams (1999), and O'Neill and Flandrin (2000) and are classified as the "quartic time-frequency distribution." The second turned out to be the Fourier transform of the quartic ambiguous ambiguity function. Using the above notions, the double dimensional extension of the Cohen's class distributions is defined and illustrated by examples.