The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform and the well-known fractional Fourier transform, has recently been demonstrated as a powerful analytical tool for signal and image processing. However, this transform suffers from a relatively poor resolution in the high fractional frequency region, which results in difficulties in discriminating signals containing close high fractional frequency components. A simple but effective method to overcome this deficiency is the fractional wavelet packet transform (FRWPT). There exist several different definitions of the FRWPT in the literature. Unfortunately, these existing definitions do not generalize well the classical results for the conventional wavelet packet transform. The objective of this paper is to obtain a novel FRWPT that preserves the properties of its conventional counterpart. We first define the novel FRWPT and then discuss its related properties. Fractional wavelet packet subspaces are also constructed. Moreover, a recursive algorithm for implementing the proposed FRWPT is presented. Finally, we discuss potential applications of the proposed FRWPT.

中文翻译：

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新型分数小波包变换：理论、实现和应用

分数小波变换 (FRWT) 概括了经典小波变换和众所周知的分数傅立叶变换，最近已被证明是一种强大的信号和图像处理分析工具。然而，这种变换在高分数频率区域的分辨率相对较差，这导致难以区分包含接近的高分数频率分量的信号。克服这一缺陷的一种简单而有效的方法是分数小波包变换 (FRWPT)。文献中有几种不同的 FRWPT 定义。不幸的是，这些现有的定义不能很好地概括传统小波包变换的经典结果。本文的目的是获得一种新颖的 FRWPT，该 FRWPT 保留了其传统对应物的特性。我们首先定义新的 FRWPT，然后讨论其相关属性。还构造了分数小波包子空间。此外，还提出了一种用于实现所提出的 FRWPT 的递归算法。最后，我们讨论了所提议的 FRWPT 的潜在应用。