电子学报 ›› 2015, Vol. 43 ›› Issue (12): 2525-2529.DOI: 10.3969/j.issn.0372-2112.2015.12.027

• 科研通信 • 上一篇    下一篇

加伯变换与线性正则变换的关系及其在滤波器设计中的应用

张志超, 罗懋康   

  1. 四川大学数学学院, 四川成都 610065
  • 收稿日期:2014-04-15 修回日期:2014-07-21 出版日期:2015-12-25 发布日期:2015-12-25
  • 通讯作者: 罗懋康
  • 作者简介:张志超 男,1991年7月生于江西省景德镇市,四川大学数学学院硕士研究生.主要研究方向为不确定性处理、信号处理.E-mail:gnsyzzc@126.com
  • 基金资助:

    国家自然科学基金(No.11171238)

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

ZHANG Zhi-chao, LUO Mao-kang   

  1. College of Mathematics, Sichuan University, Chengdu, Sichuan 610065, China
  • Received:2014-04-15 Revised:2014-07-21 Online:2015-12-25 Published:2015-12-25

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.

关键词: 加伯变换, 线性正则变换, 仿射变换

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.

Key words: Gabor transform, linear canonical transform, affine transformation

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