Generalized time-shift covariant quadratic time-frequency representations with arbitrary group delays

We propose new classes of quadratic time-frequency representations (QTFRs) that satisfy the generalized time-shift covariance property important for analyzing signals propagating through systems with group delay dependent characteristics. We obtain these classes from Cohen's (1966) class and the affine class of constant time-shift covariant QTFRs using a generalized warping that depends on the desirable group delay time-shift covariance. We develop formulations for the new classes, desirable properties with kernel constraints, new QTFR members, and intersection subclasses. We also propose the new exponential class of frequency-shift covariant and exponential time-shift covariant QTFRs.

[1]  Olivier Rioul,et al.  Time-scale energy distributions: a general class extending wavelet transforms , 1992, IEEE Trans. Signal Process..

[2]  L. Cohen.  Generalized Phase-Space Distribution Functions , 1966 .

[3]  Richard G. Baraniuk.  Warped perspectives in time-frequency analysis , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[4]  P. Bertrand,et al.  A class of affine Wigner functions with extended covariance properties , 1992 .

[5]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[6]  Antonia Papandreou-Suppappola,et al.  A unified framework for the scale covariant affine, hyperbolic, and power class quadratic time-frequency representations using generalized time shifts , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Antonia Papandreou-Suppappola,et al.  The hyperbolic class of quadratic time-frequency representations. I. Constant-Q warping, the hyperbolic paradigm, properties, and members , 1993, IEEE Trans. Signal Process..

[8]  Antonia Papandreou-Suppappola,et al.  New classes of quadratic time-frequency representations with scale covariance and generalized time-shift covariance: Analysis, detection, and estimation , 1995 .

[9]  Douglas L. Jones,et al.  Unitary equivalence: a new twist on signal processing , 1995, IEEE Trans. Signal Process..

[10]  F. Hlawatsch,et al.  The power classes of quadratic time-frequency representations: a generalization of the affine and hyperbolic classes , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.