A higher order generalization of an alias-free discrete time-frequency analysis

In this paper, we propose a novel higher order time-frequency distribution (GDH) for discrete time signals. This distribution is defined over the original discrete time-frequency grids through a delicate discretization of an equivalent expression of a higher order distribution, for continuous time signals, in [Fonollosa & Nikias 1993]. We also present a constructive design method, for the kernel of the GDH, by which the distribution satisfies (i) the alias free condition as well as (ii) the marginal conditions. A numerical example shows that the proposed distribution reasonably suppresses the artifacts which are observed severely in a simple higher order generalization of the Wigner distribution.