Power classes of quadratic time-frequency representations: A generalization of the affine and hyperbolic classes

Authors

Franz Hlawatsch, TU Wien
Antonia Papandreou, TU Wien
G. Faye Boudreaux-Bartels, TU Wien

Document Type

Conference Proceeding

Date of Original Version

12-1-1993

Abstract

The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) are frameworks for multiresolution or constant-Q time-frequency analysis. This paper generalizes the affine and hyperbolic QTFR classes by introducing the power classes (PCs) which comprise all QTFRs that are scale-covariant and covariant to power-law time shifts. The affine and hyperbolic classes are special cases of the PCs. We show that the PCs can be obtained from the affine class through a `power warping' mapping. We discuss signal transformations related to the PCs, the description of the PCs by kernel functions, desirable properties and kernel constraints, and specific PC members.

Publication Title, e.g., Journal

Conference Record of the Asilomar Conference of Signals Systems Computers

Volume

2

Citation/Publisher Attribution

Hlawatsch, Franz, Antonia Papandreou, and G. Faye Boudreaux-Bartels. "Power classes of quadratic time-frequency representations: A generalization of the affine and hyperbolic classes." Conference Record of the Asilomar Conference of Signals Systems Computers 2, (1993). https://digitalcommons.uri.edu/ele_facpubs/1601