Quadratic-phase wave-packet transform in L^2(R)
Date
2022
Authors
Srivastava, H.M.
Shah, Firdous A.
Lone, Waseem Z.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
Wavelet transform is a powerful tool for analysing the problems arising in harmonic
analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be
inadequate for representing those signals whose energy is not well concentrated in the frequency
domain. In pursuit of representations of such signals, we propose a novel time-frequency transform
coined as quadratic-phase wave packet transform in L^2(R). The proposed transform is aimed at
rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform
with extra degrees of freedom. Besides the formulation of all the fundamental results, including the
orthogonality relation, reconstruction formula and the characterization of range, we also derive a
direct relationship between the well-knownWigner-Ville distribution and the proposed transform. In
addition, we study the quadratic-phase wave-packet transform in the framework of almost periodic
functions. Finally, we extend the scope of the present work by investigating the composition of
quadratic-phase wave packet transforms.
Description
Keywords
quadratic-phase Fourier transform, wave-packet transform, Wigner-Ville distribution, periodic function, composition operator
Citation
Srivastava, H. M., Shah, F. A., & Lone, W. Z. (2022). “Quadratic-phase wavepacket transform in L2(R).” Symmetry, 14(10), 2018. https://doi.org/10.3390/sym14102018