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<p>In this present paper, we consider the generalized Weinstein operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_745_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta _{W}^{d,\alpha ,n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow> <mi>W</mi> </mrow> <mrow> <mi>d</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, we introduce and study some types of wavelet packets and the corresponding wavelet transforms. We prove for these transforms the Plancherel formulas, the reconstruction formulas and their scale discrete scaling functions.</p>

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Wavelet Packet analysis associated with the generalized Weinstein operator

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Hassen Ben Mohamed

摘要

In this present paper, we consider the generalized Weinstein operator \(\Delta _{W}^{d,\alpha ,n}\) Δ W d , α , n , we introduce and study some types of wavelet packets and the corresponding wavelet transforms. We prove for these transforms the Plancherel formulas, the reconstruction formulas and their scale discrete scaling functions.