Novel Fractional Wavelet Packet Transform: Theory, Implementation, and Applications

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.