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

doi:10.3969/j.issn.0372-2112.2015.12.027

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

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

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
- 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

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/Abstract

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

中图分类号:

TN911.7

张志超, 罗懋康. 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[J]. 电子学报, 2015, 43(12): 2525-2529.

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.

参考文献

[1] M Moshinsky,C Quesne.Linear canonical transformations and their unitary representations[J].Journal of Mathematical Physics,1971,12 (8):1772-1783.
[2] S A Collins.Lens-system diffraction integral written in terms of matrix optics[J].Journal of the Optical Society of America,1970,60 (9):1168-1177.
[3] 邓兵,陶然.线性正则变换及其应用[J].兵工学报,2006,27(4):665-670. DENG Bing,TAO Ran.Linear canonical transform and its implication[J].Acta Armamentarii,2006,27 (4):665-670.(in Chinese)
[4] B M Hennelly,J T Sheridan.Fast numerical algorithm for the linear canonical transforms[J].Journal of the Optical Society of America A,2005,22(5):928-937.
[5] B Barshan,M A Kutay,H M Ozaktas.Optimal filtering with linear canonical transformations[J].Optics Communications,1997,135(1):32-36.
[6] Soo-chang Pei,Jian-jiun Ding.Eigenfunctions of linear canonical transform[J].IEEE Transactions on Signal Processing,2002,50(1):11-26.
[7] Soo-chang Pei,Jian-jiun Ding.Close-form discrete fractional and affine Fourier transforms[J].IEEE Transactions on Signal Processing,2000,48(5):1338-1353.
[8] Soo-chang Pei,Jian-jiun Ding.Eigenfunctions of the offset Fourier,fractional Fourier,and linear canonical transforms[J].Journal of the Optical Society of America A,2003,20 (3):522-532.
[9] Jian-Jiun Ding.Research of Fractional Fourier Transform and Linear Canonical Transform[D].Taipei,Taiwan:National Taiwan University,2001.
[10] K K Sharma,S D Joshi.Signal separational using linear canonical and fractional Fourier transform[J].Optics Communications,2006,265 (2):454-460.
[11] Soo-chang Pei,Jian-jiun Ding.Relations between Gabor transforms and fraction Fourier transform and their applications for signal processing[J].IEEE Transactions on Signal Processing,2007,55 (10):4839-4850.
[12] 向强,秦开宇.基于线性正则变换与短时傅里叶变换联合的时频分析方法[J].电子学报,2011,39(7):1508-1513. XIANG Qiang,QIN Kai-yu.A time-frequency analysis method based on linear canonical transform and short-time Fourier transform[J].Acta Electronica Sinica,2011,39 (7):1508-1513.(in Chinese)
[13] 向强.线性正则变换相关理论问题研究[D].四川成都:电子科技大学,2013.38-47. XIANG Qiang.Research on Some Theoretical Issues of the Linear Canonical Transform[D].Chengdu,Sichuan:University of Electronics Science & Technology of China,2013,38-47.(in Chinese)
[14] 陶然,邓兵,王越.分数阶傅里叶变换及其应用[M].北京:清华大学出版社,2009.451-453.
[15] D Gabor.Theory of communication[J].Journal of the Institution of Electrical Engineers,1946,93(3):429-457.
[16] M J Bastiaans.Gabor's expansion of signal into Gaussian elementary signals[J].Proceedings of the IEEE,1980,68(4):594-598.

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

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

编辑推荐

Metrics

[1]	张亮, 于洪波, 张翔宇, 王国宏, 景洲. 吕分布时间尺度分析及实现方法研究[J]. 电子学报, 2022, 50(11): 2790-2798.
[2]	平强, 庄连生, 俞能海. 姿态和光照可变条件下的仿射最小线性重构误差人脸识别算法[J]. 电子学报, 2012, 40(10): 1965-1970.
[3]	向强;秦开宇. 基于线性正则变换与短时傅里叶变换联合的时频分析方法[J]. 电子学报, 2011, 39(7): 1508-1513.
[4]	向强;秦开宇;张传武. 线性正则变换域的带限信号采样理论研究[J]. 电子学报, 2010, 38(9): 1984-1989.
[5]	王沁;梁静;齐悦 . 一种有效缩减AES算法S盒面积的组合逻辑优化设计[J]. 电子学报, 2010, 38(4): 939-0942.
[6]	刘小武;陈武凡;冯衍秋. PROPELLER磁共振成像数据重建中的仿射运动校正新算法[J]. 电子学报, 2010, 38(4): 904-0909.
[7]	李炳照, 陶然, 王越. 线性正则变换域的框架理论研究[J]. 电子学报, 2007, 35(7): 1387-1390.
[8]	牛夏牧;SCHMUCKER Martin;BUSCH Christoph. 基于时间轴上模板的动态图像数字水印处理技术[J]. 电子学报, 2004, 32(8): 1236-1238.
[9]	黄旭明, 王斌, 张立明. 一种基于独立元分析的仿射不变描述和仿射变换参数估计的新方法[J]. 电子学报, 2004, 32(12): 2020-2023.
[10]	康显桂;黄继武;林彦;杨群生. 抗仿射变换的扩频图像水印算法[J]. 电子学报, 2004, 32(1): 8-12.
[11]	张立华;徐文立. 基于遗传算法的点模式匹配方法[J]. 电子学报, 2000, 28(10): 36-40.