2024 : 11 : 13
Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
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Education: PhD.
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Research

Title
LINEAR CANONICAL WAVELET FRAMES AND THEIR STABILITY
Type
JournalPaper
Keywords
Canonical Wavelet, Frame, Stability, Linear Canonical Transform, Unimodular Matrix.
Year
2024
Journal Applied and Computational Mathematics
DOI
Researchers Firdous Ahmad Shah ، Aajaz A Teali ، Asghar Rahimi

Abstract

The aim of this study is to address this issue by constructing a novel family of wavelets in L 2 (R) based on the linear canonical transform having certain extra degrees of freedom. At the outset, we present a necessary condition and three sufficient conditions for the canonical wavelet system { ψ H ma0,nb0 (t) : m, n ∈ Z, H = (A, B, C, D) } to be a frame for L 2 (R) without any decay assumptions on the generator of the system. Secondly, we show that under certain assumptions, a canonical wavelet frame remains a frame in L 2 (R) when the generator of the wavelet frame ψ or the dilation and translation parameters a0 and b0 are perturbed.