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<p>The deformed Hankel wavelet transform denoted by (<i>k</i>,&#xa0;<i>n</i>)-HWT is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of the time–frequency analysis within a short span of time. Knowing the fact that the study of wavelet packets are both theoretically interesting and practically useful, we present the construction of wavelet packets associated with the deformed Hankel transform and investigate their orthonormal properties. More precisely, we introduce some new wavelet packets, and its corresponding wavelet transformations associated to the deformed Hankel transform. We show for these transformations a Plancherel-type formulas, a reconstruction formulas with its scale discrete scaling functions.</p>

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Wavelet packets analysis for the deformed Hankel transform

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Saifallah Ghobber,
  • Hatem Mejjaoli

摘要

The deformed Hankel wavelet transform denoted by (k, n)-HWT is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of the time–frequency analysis within a short span of time. Knowing the fact that the study of wavelet packets are both theoretically interesting and practically useful, we present the construction of wavelet packets associated with the deformed Hankel transform and investigate their orthonormal properties. More precisely, we introduce some new wavelet packets, and its corresponding wavelet transformations associated to the deformed Hankel transform. We show for these transformations a Plancherel-type formulas, a reconstruction formulas with its scale discrete scaling functions.