基于实值离散Gabor变换的线性时变系统表示与逼近  

Representation and Approximation of Time-varying Systems via Real-valued Discrete Gabor Transforms

作　　者：陶亮[1] 阎军[1] 

机构地区：[1]安徽大学计算机科学与技术学院,安徽合肥230039

出　　处：《系统仿真学报》2004年第11期2391-2394,共4页Journal of System Simulation

基　　金：国家教育部优秀青年教师资助计划项目(教人司[2002]40号);安徽省自然科学基金项目(01042210);安徽省教育厅自然科学重点研究项目(2001kj020zd);安徽大学人才队伍建设经费资助。

摘　　要：基于作者先前提出的快速实值离散Gabor变换,本文提出了一有效的算法用于线性时变系统表示与逼近。系统的核表示近年来由于在线性时变系统优化设计与分析中的适用性,而受到关注,但缺点是核表示法需要很多的表示参数。系统的核实际上可看作是一二维离散时间序列(类似于一二维图像矩阵),因此,利用离散Gabor变换在时频域中对信号的压缩作用,将核变换到联合时频域中,就可在一定的系统逼近误差下获得一组紧凑的系统表示系数。所提出的算法由于采用了快速的实值离散Gabor变换,比基于传统的复值离散Gabor变换算法更快、更易于软件或硬件的实现,在时频域中系统表示系数更紧凑。实验比较结果也显示了所提出算法的有效性。An efficient algorithm for the representation and approximation of linear time-varying systems is presented, in this paper, via the fast real-valued discrete Gabor transforms proposed in our previous work. The linear time-varying system is assumed to be given in input-output or kernel representation (the kernel can actually be treated as a 2D discrete-time signal in the form of a 2D matrix like a 2D image). The kernel representation has recently received attention because of the applicability in frozen-time analysis and design of optimal control for time-varying systems, but requires a large number of coefficients. Due to its capability of signal compression, the Gabor transform is applied to transform the kernel into the joint time-frequency domain so that a compact representation of the system can be obtained through truncating the transform coefficients by using a thresholding strategy within a specified system approximation error. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm is faster. It can be implemented more easily in software or hardware and leads to a more compact representation. Experimental results have also demonstrated the efficiency of the proposed algorithm.

关 键 词：实值离散GABOR变换 核表示 线性时变系统 联合时频域 

分 类 号：TP271.71[自动化与计算机技术—检测技术与自动化装置]