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

Hlawatsch, Franz; Papandreou, A.; Boudreaux-Bartels, G.F.

doi:10.1109/acssc.1993.342332

Cited by 26 publications

(41 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The next theorem [23] establishes an important relation between any power class PC and the affine class PC . This relation is useful since it permits us to derive the theory of the PC's from the well-known theory of the affine class.…”

Section: A Power Warpingmentioning

confidence: 89%

“…We first note that any QTFR of a signal can be written in terms of a four-dimensional (4-D) kernel as [9], [32] (3) The following theorem [23], whose proof is outlined in Appendix A, gives a condition for the existence of and general expressions for QTFR's satisfying the covariance properties in (1) and (2). These expressions correspond to a special format of the 4-D kernel that is parameterized in terms of a 2-D function .…”

Section: Scale Covariance and Generalized Time-shift Covariancementioning

confidence: 99%

“…the scale covariance (1) and the power time-shift covariance (10) for any given power parameter . This QTFR class will be called the power class associated with the power parameter and abbreviated as PC [16], [17], [23]- [25]. According to (6), QTFR's of PC can be written as (12) where the 2-D kernel uniquely characterizes the PC QTFR .…”

Section: The Power Classesmentioning

confidence: 99%

“…The time-frequency geometry underlying the PC's is related to the family of power impulses defined as [23] (17) with spectral energy density and group delay . For (corresponding to the affine class), we obtain the Fourier transform of conventional Dirac impulses .…”

Section: B Power Signal Expansionmentioning

confidence: 99%

“…It will be shown that powerfunction group delays play a particularly important role for this type of QTFR's since they are the only functions that lead to maximally wide QTFR classes, i.e., QTFR classes that are parameterized by an arbitrary two-dimensional (2-D) kernel function (see Section II). This will motivate the definition of the power classes (PC's) of QTFR's, for which the group delay is described by a power function 1 [16], [17], [23]- [25]. Subsequently, the PC's will be studied in some detail.…”

mentioning

confidence: 99%

See 4 more Smart Citations

The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

Hlawatsch

Papandreou-Suppappola

Boudreaux-Bartels

1999

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

Abstract-We consider scale-covariant quadratic timefrequency representations (QTFR's) specifically suited for the analysis of signals passing through dispersive systems. These QTFR's satisfy a scale covariance property that is equal to the scale covariance property satisfied by the continuous wavelet transform and a covariance property with respect to generalized time shifts. We derive an existence/representation theorem that shows the exceptional role of time shifts corresponding to group delay functions that are proportional to powers of frequency. This motivates the definition of the power classes (PC's) of QTFR's. The PC's contain the affine QTFR class as a special case, and thus, they extend the affine class. We show that the PC's can be defined axiomatically by the two covariance properties they satisfy, or they can be obtained from the affine class through a warping transformation. We discuss signal transformations related to the PC's, the description of the PC's by kernel functions, desirable properties and kernel constraints, and specific PC members. Furthermore, we consider three important PC subclasses, one of which contains the Bertrand P k distributions. Finally, we comment on the discrete-time implementation of PC QTFR's, and we present simulation results that demonstrate the potential advantage of PC QTFR's.

show abstract

Section: A Power Warpingmentioning

confidence: 89%

Section: Scale Covariance and Generalized Time-shift Covariancementioning

confidence: 99%

Section: The Power Classesmentioning

confidence: 99%

Section: B Power Signal Expansionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

Hlawatsch

Papandreou-Suppappola

Boudreaux-Bartels

1999

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

Geometry of Affine Time–Frequency Distributions

Flandrin

Gonçalvès

1996

Applied and Computational Harmonic Analysis

View full text Add to dashboard Cite

Bertrands' bilinear affine time-frequency distributions are considered from the point of view of their geometry in the timefrequency plane. General construction rules are established for interference terms, with further interpretations in terms of localization properties, generalized means and symmetries. In the case of frequency modulated signals, it is shown how the pointwise application of these rules can be refined by the study of a critical manifold and stationary phase-type approximations. Theoretical results are supported by both analytical and numerical examples.

show abstract

Quadratic Time-Frequency Representations with Scale Covariance and Generalized Time-Shift Covariance: A Unified Framework for the Affine, Hyperbolic, and Power Classes

Papandreou-Suppappola

Hlawatsch

Boudreaux-Bartels

1998

Digital Signal Processing

View full text Add to dashboard Cite

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

Cited by 26 publications

References 12 publications

The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

Geometry of Affine Time–Frequency Distributions

Quadratic Time-Frequency Representations with Scale Covariance and Generalized Time-Shift Covariance: A Unified Framework for the Affine, Hyperbolic, and Power Classes

Contact Info

Product

Resources

About