2022/01/05 by Mohd Younus Bhat, Bhat, Mohd Younus, Aamir H. Dar +5 · 2 citations
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Machine Fault Diagnosis Techniques #Mathematical Analysis and Transform Methods #Signal Processing (eess.SP) #Ultrasonics and Acoustic Wave Propagation #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2202.12942
openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.