The power classes of quadratic time-frequency representations: a generalization of the affine and hyperbolic classes

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