A new fractional wavelet transform

被引：72

作者：

Dai, Hongzhe ^{[1
]}

Zheng, Zhibao ^{[1
]}

Wang, Wei ^{[1
]}

机构：

[1] Harbin Inst Technol, Sch Civil Engn, Harbin, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 44卷

基金：

中国国家自然科学基金;

关键词：

Fractional fourier transform; Fractional wavelet transform; Multiresolution analysis; FOURIER-TRANSFORM;

D O I：

10.1016/j.cnsns.2016.06.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：19 / 36

页数：18

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