Relations Between Gabor Transform and Linear Canonical Transform and Their Application for Filter Design

ZHANG Zhi-chao; LUO Mao-kang

doi:10.3969/j.issn.0372-2112.2015.12.027

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Relations Between Gabor Transform and Linear Canonical Transform and Their Application for Filter Design

更新时间：2025-07-16

- Relations Between Gabor Transform and Linear Canonical Transform and Their Application for Filter Design
- Acta Electronica Sinica Vol. 43, Issue 12, Pages: 2525-2529(2015)
- 作者机构：
  
  四川大学数学学院,四川,成都,610065
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11171238)
- DOI：10.3969/j.issn.0372-2112.2015.12.027
  CLC： TN911.7
- Published：2015
- 稿件说明：
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ZHANG Zhi-chao, LUO Mao-kang. Relations Between Gabor Transform and Linear Canonical Transform and Their Application for Filter Design[J]. Acta Electronica Sinica, 2015, 43(12): 2525-2529.
DOI：

ZHANG Zhi-chao, LUO Mao-kang. Relations Between Gabor Transform and Linear Canonical Transform and Their Application for Filter Design[J]. Acta Electronica Sinica, 2015, 43(12): 2525-2529. DOI： 10.3969/j.issn.0372-2112.2015.12.027.

摘要

线性正则变换是分数阶傅里叶变换的广义形式

由于其具有3个自由参数

故相比于分数阶傅里叶变换有更强的灵活性.加伯变换作为短时傅里叶变换的特例

是信号处理领域中一种重要的时频分析工具.本文基于短时傅里叶变换与线性正则变换的关系以及Gaussian函数在线性正则变换下的不变性

研究了加伯变换与线性正则变换的关系

提出了一种修正的加伯变换形式

得到了当参变量满足一定条件时修正后的加伯变换与线性正则变换之间具有时频平面仿射变换关系

进而研究了该关系在线性正则变换域上滤波器设计中的应用.仿真的结果验证了结论的正确性

表明了滤波器设计方法的有效性.

Abstract

The linear canonical transform(LCT)is a generalization of the fractional Fourier transform(FRFT)and has more flexibility than FRFT sinice it contains three free parameters.As a special case of the short-time Fourier transform(STFT)

the Gabor transform(GT)is an important time-frequency analysis tool for signal processing.According to the relationship between STFT and LCT

as well as the invariance of Gaussian function in LCT domain

we present a new form of GT and obtain that the LCT is equivalent to an affine transformation for the new GT when parameters meet certain conditions.Furthermore

we investigate the application of this relationship for filter design in LCT domain.Finally

the simulation results verify the correctness and effectiveness of the proposed theory and technique.

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Related Institution

（南方医科大学生物医学工程学院医学信息研究所，）

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Fraunhofer Institute for Computer Graphics (IGD)Fraunhoferstr 5D- DarmstadtGermany

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Fraunhofer Institute for Computer Graphics (IGD),Fraunhoferstr 5,- Darmstadt

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