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Using the Lambert-W Function to Create a New Class of Warped Time-Frequency Representations

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Abstract

In this paper, we propose a new warping function to create a new class of warped time-frequency representations (TFRs). We provide the formula for the derivative warping function and its inverse which is defined using the Lambert-W function. Examples are provided demonstrating how the new warping function can be successfully used on wide variety of nonlinear FM chirp signals to linearize their support in the warped time-frequency plane. An algorithm is proposed to optimize the parameter of the new warping function. We also formulate nonlinear FM chirp signals that are ideally matched to this new class of TFRs. These matched FM chirp signals have highly concentrated warped TFRs and no inner-interference terms.

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Authors and Affiliations

  1. Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI, 02881, USA

    Amal Feltane, G. Faye Boudreaux-Bartels & Yacine Boudria

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  1. Amal Feltane
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  2. G. Faye Boudreaux-Bartels
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  3. Yacine Boudria
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Correspondence to Amal Feltane.

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Feltane, A., Boudreaux-Bartels, G.F. & Boudria, Y. Using the Lambert-W Function to Create a New Class of Warped Time-Frequency Representations. Circuits Syst Signal Process 37, 3191–3205 (2018). https://doi.org/10.1007/s00034-017-0733-0

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  • DOI: https://doi.org/10.1007/s00034-017-0733-0

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