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arXiv · 1811.04601

Generalized Born--Jordan Distributions and Applications

Elena Cordero·Maurice de Gosson·Monika Dörfler·Fabio Nicola
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Abstract

The quadratic nature of the Wigner distribution causes the appearance of unwanted interferences. This is the reason why engineers, mathematicians and physicists look for related time-frequency distributions, many of them are members of the Cohen class. Among them, the Born-Jordan distribution has recently attracted the attention of many authors, since the so-called ghost frequencies are damped quite well, and the noise is in general reduced. The very insight relies on the kernel of such a distribution, which contains the sinus cardinalis (sinc), which can be viewed as the Fourier transform, of the first B-Spline. Replacing the function B-Spline with the spline or order n, on the Fourier side we obtain the n-th power of sinc, whose decay at infinity increases with n. We introduce the corresponding Cohen's Kernel and study the properties of the related time-frequency distribution which we call generalized Born--Jordan distribution.

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Elena Cordero, Maurice de Gosson, Monika Dörfler, Fabio Nicola. 2018-11-12. Generalized Born--Jordan Distributions and Applications. https://arxiv.org/abs/1811.04601

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