New higher order affine time-frequency representations

Document Type

Conference Proceeding

Date of Original Version



In the same spirit that the quadratic Wigner distribution and the Altes-Marinovic Q-distribution were extended to higher order time-frequency representations, we propose the new higher order Bertrand P0-distribution (HO-P0D), as an extension of the quadratic Bertrand P0-distribution. We show that the new HO-P0D preserves scale changes, and up to a known sign, constant time and hyperbolic time shifts on the signal. We also discuss the importance of the new HO-P0D, derive some of its desirable properties, discuss its limitations, and derive a higher order class consisting of smoothed HO-P0Ds. Finally, we propose a formulation for a higher order extension of the quadratic affine class which preserves scale changes and constant time shifts.

Publication Title

Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

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