Quadratic-phase wave packet transform
Bhat M.Y. Dar A.H. Urynbassarova D. Urynbassarova A.
July 2022Elsevier GmbH
Optik
2022#261
The quadratic-phase Fourier transform (QPFT) 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 give 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.
Energy conservation , Quadratic-phase Fourier transform , Quadratic-phase wave packet transform , Uncertainty inequality
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Department of Mathematical Sciences, Islamic University of Science and Technology Awantipora, Jammu and Kashmir, Pulwama, 192122, India
School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, China
Beijing Key Laboratory of Fractional Signals and Systems, Beijing, 100081, China
Department of Technology and Ecology, School of Society, Technology and Ecology, Narxoz University, Almaty, 050000, Kazakhstan
Department of Information Security, Faculty of Information Technology, L.N. Gumilyov Eurasian National University, Nur-Sultan, 010000, Kazakhstan
Department of Mathematical Sciences
School of Information and Electronics
Beijing Key Laboratory of Fractional Signals and Systems
Department of Technology and Ecology
Department of Information Security
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