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

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 fu...

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Bibliographic Details
Published in:Circuits, systems, and signal processing systems, and signal processing, 2018-08, Vol.37 (8), p.3191-3205
Main Authors: Feltane, Amal, Boudreaux-Bartels, G. Faye, Boudria, Yacine
Format: Article
Language:English
Subjects:
Chirp signals
Circuits and Systems
Electrical Engineering
Electronics and Microelectronics
Engineering
Instrumentation
Parameter optimization
Representations
Signal,Image and Speech Processing
Warping
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Summary: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.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-017-0733-0