Differential Operator and the Construction of Wavelet

YUAN Xiao; CHEN Xiang-dong; LI Qi-liang; ZHANG Shu-ping; JIANG Ya-dong; YU Jue-bang

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Differential Operator and the Construction of Wavelet

更新时间：2025-07-16

- Differential Operator and the Construction of Wavelet
- Acta Electronica Sinica Vol. 30, Issue 5, Pages: 769-773(2002)
- 作者机构：
  
  1. 四川大学电子信息学院,四川,成都,610064
  2. 电子科技大学传感技术工程四川省重点实验室,四川,成都,610054
  3. 空军工程大学航空电子工程系,陕西,西安,710038
  4. 四川大学物理学院,四川,成都,610064
  5. 电子科技大学电子工程学院,四川,成都,610054
  6. 四川大学电子信息学院四川成都,610064
  7. 电子科技大学传感技术工程四川省重点实验室四川成都,610054
  8. 空军工程大学航空电子工程系陕西西安,710038
  9. 四川大学物理学院四川成都,610064
  10. 电子科技大学电子工程学院四川成都,610054
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN941
- Published：2002
- 稿件说明：
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YUAN Xiao, CHEN Xiang-dong, LI Qi-liang, et al. Differential Operator and the Construction of Wavelet[J]. Acta Electronica Sinica, 2002, 30(5): 769-773.
DOI：

YUAN Xiao, CHEN Xiang-dong, LI Qi-liang, et al. Differential Operator and the Construction of Wavelet[J]. Acta Electronica Sinica, 2002, 30(5): 769-773. DOI：

摘要

将传统意义下的整数阶微分运算拓展到非整数阶微分情形

直接仿照整数阶微分在时域的极限定义形式是很困难的.本文从分析微分运算的频域形式着手

将微分算子分解成幅度算子和相位算子

并将其与子波变换特征进行比照研究

从而解决了非整数阶微分的拓展问题

同时也得到了微分运算与子波变换的内在联系

为非整数阶微分计算提供了一种逼近方式.文中提出了幅度算子、广义Hilbert变换等新概念并重点探讨了基于非整数阶微分运算的子波构造及其局域化特征等问题.

Abstract

This paper investigates the topic of non-integral order differentiation.Following directly the limit definition of the classical integral order differentiation in the time-domain

it is difficult to expand the classical differential operation from the integral order case to the non-integral order case.Based on the expression of differential operation in the frequency domain

and wedding it to the wavelet transform

the non-integral order differential problem was solved in this paper.Meanwhile the inherent law between the non-integral order differential operation and the wavelet transform was discovered

and an approximate approach for computing the non-integral order differentiation was given.In this paper we introduce some new concepts

such as the magnitude operator and the generalized Hilbert transform etc

thereby study emphatically the construction and the localization characteristics of wavelet which is based on the non-integral order differentiation of a low-pass function.

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