加权分数傅里叶变换在采样重构中的应用  

Application of weighted-type fractional Fourier transform in sampling and reconstruction

作　　者：史军[1] 迟永钢[1] 沙学军[1] 张乃通[1] 

机构地区：[1]哈尔滨工业大学通信技术研究所,黑龙江哈尔滨150001

出　　处：《通信学报》2010年第4期88-93,共6页Journal on Communications

基　　金：国家重点基础研究发展计划("973"计划)资助项目(2007CB310606);新一代宽带无线移动通信网科技重大专项基金资助项目(2009ZX03004-001);黑龙江省自然科学基金资助项目(F200906)~~

摘　　要：针对频域非带限信号的重构问题,提出了一种基于加权分数傅里叶变换的采样与重构算法,并利用信号加权分数傅里叶变换在加权分数域的特性,得到了信号可完全重构的条件。理论分析和仿真结果表明,在满足给定误差的条件下,该算法能够以低于香农重构所需的采样率实现对信号的恢复,且简单易行,可利用FFT快速算法实现。A new sampling and reconstruction scheme based on the weighted-type fractional Fourier transform （WFRFT） was proposed for a class of signals which were nonbandlimited in the frequency domain. Based on the representation of the signal in the WFRFT domain, conditions under which exact recovery of the signal is possible were derived. Theoreti- cal analysis and simulation results show that the proposed scheme can perfectly recover signal below the sampling rate of Shannon reconstruction within the given error tolerance, and it can be implemented efficiently with the fast Fourier transform （FFT） algorithm.

关 键 词：分数傅里叶变换 加权分数傅里叶变换 采样定理 信号重构 

分 类 号：TN911[电子电信—通信与信息系统]