A unified framework for the scale covariant affine, hyperbolic, and power class quadratic time-frequency representations using generalized time shifts

  • Authors:

  • A. Papandreou;F. Hlawatsch;G. F. Boudreauz-Bartels

  • Affiliations:

  • Dept. of Electr. Eng., Rhode Island Univ., Kingston, RI, USA;Dept. of Electr. Eng., Pittsburgh Univ., PA, USA;Dept. of Inf. Eng., Ryukyus Univ., Okinawa, Japan

  • Venue:
  • ICASSP '95 Proceedings of the Acoustics, Speech, and Signal Processing, 1995. on International Conference - Volume 02
  • Year:
  • 1995

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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.