Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3191–3205 | Cite as

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

  • Amal FeltaneEmail author
  • G. Faye Boudreaux-Bartels
  • Yacine Boudria


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.


Warping function TFRs Lambert-W function FM chirp signal 


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Amal Feltane
    • 1
    Email author
  • G. Faye Boudreaux-Bartels
    • 1
  • Yacine Boudria
    • 1
  1. 1.Department of Electrical, Computer, and Biomedical EngineeringUniversity of Rhode IslandKingstonUSA

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