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

被引：0
作者：
Amal Feltane
G. Faye Boudreaux-Bartels
Yacine Boudria
机构：
[1] University of Rhode Island,Department of Electrical, Computer, and Biomedical Engineering
来源：
Circuits, Systems, and Signal Processing | 2018年 / 37卷
关键词：
Warping function; TFRs; Lambert-W function; FM chirp signal;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：3191 / 3205
页数：14
相关论文
共 39 条
[1]  
Baraniuk RG(1995)Unitary equivalence: a new twist on signal processing IEEE Trans. Signal Process. 43 2269-2282
[2]  
Baraniuk RG(2001)Measuring time-frequency information content using the Rényi entropies IEEE Trans. Inf. Theory 47 1391-1409
[3]  
Flandrin P(1992)A class of affine wigner functions with extended covariance properties J. Math. Phys. 33 2515-2527
[4]  
Janssen AJ(1994)Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra IEEE Trans. Signal Process. 42 216-220
[5]  
Michel OJ(1989)Time-frequency distributions: a review Proc. IEEE 77 941-981
[6]  
Bertrand J(1996)On the Lambert W function Adv. Comput. Math. 5 329-359
[7]  
Bertrand P(1992)Linear and quadratic time-frequency signal representations IEEE Signal Process. Mag. 9 21-67
[8]  
Boashash B(1997)The hyperbolic class of quadratic time-frequency representations-part II: subclasses, intersection with the affine and power classes, regularity and unitarity IEEE Trans. Signal Process. 45 303-315
[9]  
O’Shea P(1999)The power classes—quadratic time-frequency representations with scale covariance and dispersive time-shift covariance IEEE Trans. Signal Process. 47 3067-3083
[10]  
Cohen L(2007)Toward the use of the time warping principle with discrete time sequences J. Comput. 2 49-55
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