Covariance Property

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 90 Experts worldwide ranked by ideXlab platform

Francesco De Martini - One of the best experts on this subject based on the ideXlab platform.

Nicolò Spagnolo - One of the best experts on this subject based on the ideXlab platform.

Fabio Sciarrino - One of the best experts on this subject based on the ideXlab platform.

F. Hlawatsch - One of the best experts on this subject based on the ideXlab platform.

  • The power classes-quadratic time-frequency representations with scale Covariance and dispersive time-shift Covariance
    IEEE Transactions on Signal Processing, 1999
    Co-Authors: F. Hlawatsch, Antonia Papandreou-suppappola, G.f. Boudreaux-bartels
    Abstract:

    We consider scale-covariant quadratic time-frequency representations (QTFRs) specifically suited for the analysis of signals passing through dispersive systems. These QTFRs 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 (PCs) of QTFR's. The PCs contain the affine QTFR class as a special case, and thus, they extend the affine class. We show that the PCs 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 PCs, the description of the PCs 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 (1992) P/sub k/ distributions. Finally, we comment on the discrete-time implementation of PC QTFRs, and we present simulation results that demonstrate the potential advantage of PC QTFRs.

  • Quadratic Time-Frequency Representations with Scale Covariance and Generalized Time-Shift Covariance: A Unified Framework for the Affine, Hyperbolic, and Power Classes☆☆☆
    Digital Signal Processing, 1998
    Co-Authors: Antonia Papandreou-suppappola, F. Hlawatsch, G.f. Boudreaux-bartels
    Abstract:

    Abstract We propose the generalized class of quadratic time-frequency representations (QTFRs) that satisfy the scale Covariance Property, which is important in multiresolution analysis, and the generalized time-shift Covariance Property, which is important in the analysis of signals propagating through systems with specific dispersive characteristics. We discuss a formulation of the generalized class QTFRs in terms of two-dimensional kernel functions, a generalized signal expansion related to the generalized class time-frequency geometry, an important member of the generalized class, a set of desirable QTFR properties and their corresponding kernel constraints, and a “localized-kernel” generalized subclass that is characterized by one-dimensional kernels. Special cases of the generalized QTFR class include the affine class and the new hyperbolic class and power classes. All these QTFR classes satisfy the scale Covariance Property. In addition, the affine QTFRs are covariant to constant time shifts, the hyperbolic QTFRs are covariant to hyperbolic time shifts, and the power QTFRs are covariant to power time shifts. We present a detailed study of these classes that includes their definition and formulation, an associated generalized signal expansion, important class members, desirable QTFR properties and corresponding kernel constraints, and localized-kernel subclasses. Also, we investigate the subclasses formed by the intersection between the affine and hyperbolic classes, the affine and power classes, and the hyperbolic and power classes. These subclasses are important since their members satisfy additional desirable properties. We show that the hyperbolic class is obtained from Cohen's QTFR class using a “hyperbolic time-frequency warping” and that the power classes are obtained similarly by applying a “power time-frequency warping” to the affine class. The affine class is a special case of the power classes. Furthermore, we generalize the time-frequency warping so that when applied either to Cohen's class or to the affine class, it yields QTFRs that are always generalized time-shift covariant but not necessarily scale covariant.

  • A UNIFIED FRAMEWORK FOR THE SCALE COVARIANT AFFINE, HYPERBOLIC, AND POWER CLASS USING GENERALIZED TIME SHIFTS* QUADRATIC TIME-FREQUENCY REPRESENTATIONS
    1995
    Co-Authors: A. Papandreoul, F. Hlawatsch, G. F. Boudreaux-bartelsl
    Abstract:

    We propose a framework that unifies and extends the affine, hyperbolic, a,nd power classes of quadratic time-frequency representa.tions (QTFRs). These QTFR classes satisfy the scale Covariance Property, important in multiresolution analysis, and a generalized time-shift Covariance Property, important in the analysis of signals propagating through dispersive systems. We provide a general class formulation in terms of 2-D kernels, a generalized signal expansion, a list of desirable QTFR properties with kernel constraints, and a “central QTFR generalizing the Wigner distribution and the Altes-Marinovich Q-distribution. We also propose two generalizled time-shift covariant (not, in general, scale covariant) QTFR classes by applying a generalized warping to Cohen’s class and to the affine class.

  • ICASSP - A unified framework for the scale covariant affine, hyperbolic, and power class quadratic time-frequency representations using generalized time shifts
    1995 International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: A. Papandreou, F. Hlawatsch, G.f. Boudreauz-bartels
    Abstract:

    We propose a framework that unifies and extends the affine, hyperbolic, and power classes of quadratic time-frequency representations (QTFRs). These QTFR classes satisfy the scale Covariance Property, important in multiresolution analysis, and a generalized time-shift Covariance Property, important in the analysis of signals propagating through dispersive systems. We provide a general class formulation in terms of 2-D kernels, a generalized signal expansion, a list of desirable QTFR properties with kernel constraints, and a "central QTFR" generalizing the Wigner distribution and the Altes-Marinovich Q-distribution. We also propose two generalized time-shift covariant (not, in general, scale covariant) QTFR classes by applying a generalized warping to Cohen's (1966) class and to the affine class.

  • ICASSP - Displacement-covariant time-frequency energy distributions
    1995 International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: F. Hlawatsch, Helmut Bölcskei
    Abstract:

    Important classes of quadratic time-frequency representations (QTFRs), such as Cohen's (1966) class and the affine, hyperbolic, and power classes, are special cases within a general theory of displacement-covariant QTFRs. We present a theory of quadratic time-frequency energy distributions that satisfy a Covariance Property and generalized marginal properties. The theory coincides with the characteristic function method of Cohen and Baraniuk (see Proc. ICASSP-94, vol.3, p.357-360, 1994) in the special case of "conjugate operators".

G.f. Boudreaux-bartels - One of the best experts on this subject based on the ideXlab platform.

  • The power classes-quadratic time-frequency representations with scale Covariance and dispersive time-shift Covariance
    IEEE Transactions on Signal Processing, 1999
    Co-Authors: F. Hlawatsch, Antonia Papandreou-suppappola, G.f. Boudreaux-bartels
    Abstract:

    We consider scale-covariant quadratic time-frequency representations (QTFRs) specifically suited for the analysis of signals passing through dispersive systems. These QTFRs 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 (PCs) of QTFR's. The PCs contain the affine QTFR class as a special case, and thus, they extend the affine class. We show that the PCs 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 PCs, the description of the PCs 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 (1992) P/sub k/ distributions. Finally, we comment on the discrete-time implementation of PC QTFRs, and we present simulation results that demonstrate the potential advantage of PC QTFRs.

  • Quadratic Time-Frequency Representations with Scale Covariance and Generalized Time-Shift Covariance: A Unified Framework for the Affine, Hyperbolic, and Power Classes☆☆☆
    Digital Signal Processing, 1998
    Co-Authors: Antonia Papandreou-suppappola, F. Hlawatsch, G.f. Boudreaux-bartels
    Abstract:

    Abstract We propose the generalized class of quadratic time-frequency representations (QTFRs) that satisfy the scale Covariance Property, which is important in multiresolution analysis, and the generalized time-shift Covariance Property, which is important in the analysis of signals propagating through systems with specific dispersive characteristics. We discuss a formulation of the generalized class QTFRs in terms of two-dimensional kernel functions, a generalized signal expansion related to the generalized class time-frequency geometry, an important member of the generalized class, a set of desirable QTFR properties and their corresponding kernel constraints, and a “localized-kernel” generalized subclass that is characterized by one-dimensional kernels. Special cases of the generalized QTFR class include the affine class and the new hyperbolic class and power classes. All these QTFR classes satisfy the scale Covariance Property. In addition, the affine QTFRs are covariant to constant time shifts, the hyperbolic QTFRs are covariant to hyperbolic time shifts, and the power QTFRs are covariant to power time shifts. We present a detailed study of these classes that includes their definition and formulation, an associated generalized signal expansion, important class members, desirable QTFR properties and corresponding kernel constraints, and localized-kernel subclasses. Also, we investigate the subclasses formed by the intersection between the affine and hyperbolic classes, the affine and power classes, and the hyperbolic and power classes. These subclasses are important since their members satisfy additional desirable properties. We show that the hyperbolic class is obtained from Cohen's QTFR class using a “hyperbolic time-frequency warping” and that the power classes are obtained similarly by applying a “power time-frequency warping” to the affine class. The affine class is a special case of the power classes. Furthermore, we generalize the time-frequency warping so that when applied either to Cohen's class or to the affine class, it yields QTFRs that are always generalized time-shift covariant but not necessarily scale covariant.

  • The effect of mismatching analysis signals and time-frequency representations
    Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), 1
    Co-Authors: Antonia Papandreou-suppappola, G.f. Boudreaux-bartels
    Abstract:

    We study the time-frequency geometry underlying quadratic time-frequency representations (QTFRs) defined based on a generalized time-shift Covariance Property. These QTFRs include the generalized warped Wigner distribution (WD) and its smoothed versions that are useful for reducing cross terms in multicomponent signal analysis applications. The generalized warped WD is ideal for analyzing nonstationary signals whose group delay matches the specified time-shift Covariance. Its smoothed versions may also be well suited for various signals provided that their smoothing characteristics match the signal's time-frequency structure. Thus, we examine the effects of a mismatch between the analysis signal and the chosen QTFR. We provide examples to demonstrate the advantage of matching the signal's group delay with the generalized time-shift Covariance Property of a given class of QTFRs, and to demonstrate that mismatch can cause significant distortion.

Related terms

Covariance Property - 15 days free trial to Access Experts & Abstracts