长序列与无限序列的多窗口实值Gabor变换优化

研究论文

177 浏览量更新于2024-08-27 收藏 408KB PDF 举报

身份认证购VIP最低享 7 折!

30元优惠券

资源详情

资源推荐

Multi-window Real-valued Discrete Gabor Transform

for Long and Infinite Sequences

Liang Tao

School of Computer Science and Technology

Anhui University

Hefei, Anhui 230039, China

taoliang@ahu.edu.cn

H. K. Kwan

Dept. of Electrical and Computer Engineering

University of Windsor

401 Sunset Avenue, Windsor, Ontario, Canada N9B 3P4

kwan1@uwindsor.ca

Abstract—The length of windows used in the existing multi-

window complex-valued discrete Gabor transform (M-CDGT) is

restricted to be the length of analyzed sequences. Consequently, if

the lengths of analyzed sequences are long, to solve the windows

requires high computation burden and memory and even leads to

numerical instability. To overcome this problem, a multi-window

real-valued discrete Gabor transform (M-RDGT) for long and

infinite sequences is presented in this paper based on the

biorthogonal analysis approach, and its corresponding

biorthogonality constraint between analysis windows and

synthesis windows is derived. The lengths of the analysis and

synthesis windows are independent of the lengths of analyzed

sequences so that one can apply finite (or short) windows to

process any long (or even infinite) sequences. The completeness

condition of the M-RDGT is proved to be equivalent to its

biorthogonality constraint between analysis windows and

synthesis windows. In addition, the M-RDGT can utilize the fast

discrete Hartley transform algorithms for fast computation and

has a simple relationship with the M-CDGT such that the M-

CDGT coefficients can be directly computed from the M-RDGT

coefficients.

Keywords—discrete Gabor transform; multi-window; discrete

Hartley transform; biorthogonality; synthesis window; analysis

window.

I. INTRODUCTION

The Gabor transform [1] has been recognized as being

useful in diverse areas such as order tracking in mechanical

systems, system identification, speech and image processing,

radar data processing, sonar and seismic data processing and

interpretation; However, the traditional Gabor transform with a

single window [2-4] suffers a limitation of the constrained

time-frequency localization governed by the Heisenberg

uncertainty principle and thus it is not enough to analyze the

dynamic time-frequency contents of signals that contain a wide

range of time and frequency components, the resolution of

which is usually low. Therefore, the complex-valued discrete

Gabor transform with multi-windows (M-CDGT) based on the

frame theory were presented in several references such as [5-

9]. Some typical applications for evolutionary spectral analysis

and macromolecular sequence analysis can be found in [7] and

[9], respectively.

However, complex-valued Gabor transforms are complex

to be implemented in software or hardware compared with the

real-valued Gabor transforms and the computational load also

increases with the number of windows used in M-CDGT. For

real-valued signals, an alternate real-valued formulation of the

M-CDGT permits a computationally efficient implementation

[4]. In addition, the existing M-CDGT can only deal with the

finite (short) sequences. The analyzed sequences, analysis and

synthesis windows in the finite M-CDGT must have an equal

length. But, in some real applications, this is quite inconvenient

and even impractical because the lengths of the analyzed

sequences could be long, the number of either analysis

windows or synthesis windows is more than one, and to solve

the windows requires huge computation time and memory and

sometime leads to numerical instability. In such cases, the

existing finite M-CDGT is no longer adequate. To overcome

this problem, we will present a new multi-window real-valued

discrete Gabor transform (M-RDGT) for the long or infinite

sequences based on the biorthogonal analysis approach similar

to that proposed in [2-3]. In the M-RDGT, the lengths of the

analysis and synthesis windows are independent of the lengths

of the analyzed sequences so that one can apply finite (or short)

windows to process any long (even infinite) sequences. We

will prove that the completeness condition of the M-RDGT is

equivalent to its biorthogonality constraint between analysis

windows and synthesis windows. The M-RDGT is defined by

replacing the complex-valued Gabor basis functions (kernels of

the discrete Fourier transform (DFT)) of M-CDGT with real-

valued Gabor basis functions (kernels of the discrete Hartley

transform (DHT)), which allows the M-RDGT to utilize the

fast DHT algorithms [10-11] for fast computation. Moreover,

the M-RDGT has a simple relationship with the M-CDGT such

that the M-CDGT coefficients can be directly computed from

the M-RDGT coefficients. Therefore, the M-RDGT also offers

an efficient method to compute the M-CDGT.

II. M-RDGT

FOR LONG OR INFINITE SEQUENCES

A. Definition of M-RDGT

Suppose that P is the number of synthesis windows

][

)(

and analysis windows ][

)(

(

10 −≤≤ Pp

), the

length of a real finite sequence x[k] is L

, and the lengths of

This work was supported in part by the National Natural Science

Foundation of China under Grant No. 61372137.

下载后可阅读完整内容，剩余3页未读，立即下载

weixin_38699302

粉丝: 2
资源: 923

长序列与无限序列的多窗口实值Gabor变换优化

实值离散Gabor变换

论文研究-实值离散Gabor变换窗函数的快速求解方法.pdf

小波变换和Gabor变换的区别

短时傅里叶变换和Gabor变换的区别

Gabor变换的MATLAB实现

matlab gabor变换

matlab gabor变换时频分析

通过MATLAB对TXT文件中的数据进行Gabor变换的代码

基于Gabor变换人脸识别系统的发展背景

基于Gabor变换的人脸识别系统的·发展前景

基于python的图像Gabor变换及特征提取

为什么gabor小波是特殊的小波变换？小波变换有哪些，Gabor小波属于哪种小波变换

在MATLAB中，你可以使用gaborfilt函数来对一维信号进行Gabor变换应该如何编写代码

基于Gabor变换的人脸识别系统设计

能写出Gabor变换的Python代码么

在MATLAB中用Gabor变换对图像中不同方向的直线进行提取

gabor变换python

Gabor变换如何结合小波变换使用

基于Gabor变换的纹理图像分割

Gabor变换在图像处理方面有哪些改进方法

最新资源