基于多抽样率滤波实现离散Gabor展开与变换的快速并行算法  

Fast parallel algorithms for discrete Gabor expansion and transform based on multirate filtering

作　　者：陶亮[1] 顾涓涓[2] 

机构地区：[1]安徽大学计算机科学与技术学院,合肥230039 [2]合肥学院电子信息与电气工程系,合肥230022

出　　处：《中国科学：信息科学》2011年第5期617-625,共9页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:61071169);安徽省人才开发资金(引进海外留学人才基金)(批准号:2005Z029);安徽省高校省级自然科学重点研究项目(批准号:KJ2010A290);安徽省电子制约技术重点实验室基金资助

摘　　要：Gabor变换在信号处理领域一直被认为是一十分有用的时频分析工具,却因Gabor变换算法的高计算复杂性而限制了其实时应用.本文基于多抽样率滤波原理,设计了分析和综合滤波器组分别用于实现离散Gabor变换与展开,从而提出了全新的离散Gabor展开与变换快速并行算法.所设计的分析和综合滤波器组中的每一并行通道具有一致的结构并能够利用快速Fourier变换(FFT)及其逆变换(IFFT)减小计算量.每一并行通道计算复杂性非常小,只取决于输入离散信号的长度及Gabor频率抽样点数,并且每一并行通道计算复杂性不会随Gabor变换过抽样率增加而增大.本文对所提出的并行算法的计算复杂性进行了分析并与目前主要的离散Gabor展开与变换并行算法进行了比较,结果表明所提出基于多抽样率滤波实现离散Gabor展开与变换的并行算法对实时信号处理十分有利.The Gabor transform has long been recognized as a very useful tool for the joint time and frequency analysis in signal processing. Its real time applications, however, were limited due to the high computational complexity of the Gabor transform algorithms. In this paper, some novel and fast parallel algorithms for the finite discrete Gabor expansion and transform are presented based on multirate filtering. An analysis filter bank is designed for the finite discrete Gabor transform （DGT） and a synthesis filter bank is designed for the finite discrete Gabor expansion （DGE）. Each of the parallel channels in the two filter banks has a unified structure and can apply the FFT and the IFFT to reduce its computational load. The computational complexity of each parallel channel does not change as the oversampling rate increases. In fact, it is very low and depends only on the length of the input discrete signal and the number of the Gabor frequency sampling points. The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the major existing parallel algorithms for the finite DGT and DGE. The results indicate that the proposed parallel algorithms for the finite DGT and DGE based on multirate filtering are very attractive for real time signal processing.

关 键 词：离散Gabor展开 离散GABOR变换 多抽样率滤波 滤波器组 

分 类 号：TN911.7[电子电信—通信与信息系统]