Executive Summary : | Dunkl operators are differential-difference operators with finite reflection groups in a Euclidean space. The fractional Dunkl transform (FRDT) is a generalization of well-known signal processing operations, such as the Fourier transform, FRFT, Fresnel transform, Hankel transform, fractional Hankel transform, and Dunkl transform. FRDT finds applications in optical systems, filter design, time-frequency analysis, and more. The wavelet transform (WT) is a growing tool in optics and signal processing, used for time-frequency analysis and image processing. FRWT, based on the fractional Fourier transform, is useful for signal processing, data compression, pattern recognition, and computer graphics. A novel fractional Dunkl wavelet transform (FRDWT) combines the advantages of the WT and FRDT, providing multiresolution analysis and signal representation in the fractional domain. FRDT is more flexible due to its one extra degree of freedom and can be used frequently in time-frequency analysis and non-stationary signal processing. Inspired by FRWT, the concept of FRDWT is introduced, inheriting the advantages of multiresolution analysis from the WT and offering signal representations in the fractional Dunkl transform domain. |