一种新型分数阶小波变换及其应用

A novel fractional wavelet transform and its applications

小波变换和分数Fourier变换是应用非常广泛的信号处理工具.但是,小波变换仅局限于时频域分析信号;分数Fourier变换虽突破了时频域局限能够在分数域分析信号,却无法表征信号局部特征.为此,提出了一种新型分数阶小波变换,该变换不但继承了小波变换多分辨分析的优点,而且具有分数Fourier变换分数域表征功能.与现有分数阶小波变换相比,新型分数阶小波变换可以实现对信号在时间-分数频域的多分辨分析.此外,该变换具有物理意义明确和计算复杂度低的优点,更有利于满足实际应用需求.最后,通过仿真实验验证了所提理论的有效性.

The wavelet transform （WT） and the fractional Fourier transform （FRFT） are powerful tools for many applications in the field of signal processing. However, the signal analysis capability of the former is limited in the time-frequency plane. Although the latter has overcome such limitation and can provide signal representations in the fractional domain, it fails in obtaining local structures of the signal. In this paper, a novel fractional wavelet transform （FRWT） is proposed in order to rectify the limitations of the WT and the FRFT. The proposed transform not only inherits the advantages of nmltiresolution analysis of the WT, but also has the capability of signal representations in the fractional domain which is similar to the FRFT. Compared with the existing FRWT, the novel FRWT can offer signal representations in the time-fractional-frequency plane. Besides, it has explicit physical interpretation, low computational complexity and usefulness for practical applications. The validity of the theoretical derivations is demonstrated via simulations.