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Electrical Engineering and Systems Science > Signal Processing

arXiv:2202.12942 (eess)
[Submitted on 5 Jan 2022]

Title:Quadratic phase wave packet transform

Authors:Mohd Younus Bhat, Aamir Hamid Dar, Didar Urynbassarova, Altyn Urynbassarova
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Abstract:The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in some applications. In this paper, the quadratic phase wave packet transform QP WPT is proposed to address this problem, based on the wave packet transform WPT and QPFT. Firstly, we propose the definition of the QP WPT and gave its relation with windowed Fourier transform WFT. Secondly, several notable inequalities and important properties of newly defined QP WPT, such as boundedness, reconstruction formula, Moyals formula, Reproducing kernel are derived. Finally, we formulate several classes of uncertainty inequalities such as Leibs uncertainty principle, logarithmic uncertainty inequality and the Heisenberg uncertainty inequality.
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT); Functional Analysis (math.FA)
Cite as: arXiv:2202.12942 [eess.SP]
  (or arXiv:2202.12942v1 [eess.SP] for this version)
  https://doi.org/10.48550/arXiv.2202.12942

Submission history

From: Mohammad Younus Bhat [view email]
[v1] Wed, 5 Jan 2022 15:31:25 UTC (13 KB)
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