On the local frequency, group shift, and cross-terms in some multidimensional time-frequency distributions: a method for multidimensional time-frequency analysis

Presents an analysis of the representation of local frequency and group shift using multidimensional time-frequency distributions. In the second part of the correspondence, the authors extend the analysis to the multicomponent signals and cross-terms effects. On the basis of that analysis, an efficient method, derived from the analysis of the multidimensional Wigner distribution defined in the frequency domain, is proposed. This method provides some substantial advantages over the Wigner distribution: the well known cross-terms effects are reduced or completely removed; the oversampling of signals is shown to be unnecessary; and the computation time can be significantly reduced, as well. The theory is illustrated by a two-dimensional numerical example.