分数傅里叶变换域稀疏带限信号的模拟信息转换  

Analog to information conversion for sparse signals band-limited in fractional Fourier transform domain

作　　者：宋维斌 张圣儒 邓忆秋 孙楠 史军[1] Song Weibin;Zhang Shengru;Deng Yiqiu;Sun Nan;Shi Jun(Communication Research Center, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China)

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：《光电工程》2018年第6期46-54,共9页Opto-Electronic Engineering

基　　金：国家自然科学基金项目(61501144);中央高校基本科研业务费专项资金项目(01111305)~~

摘　　要：经典香农采样定理在信号处理和通信领域有着深远的影响,随着高速率采样与转换精度矛盾的日益突出,基于香农采样定理的传统模拟数字转换技术面临严峻的挑战,尤其是在降低采样率问题上存在着瓶颈效应的制约。近年来,在信号处理领域诞生的基于压缩感知理论的模拟信息转换技术为解决这一问题提供了一种有效的办法。然而,现有模拟信息转换的信号模型仅适合频域带限的多音和多带信号。在通信、雷达等电子信息系统广泛存在的线性调频信号就不满足这一模型。鉴于此,本文提出了基于分数傅里叶变换的模拟信息转换,不仅对现有模拟信息转换在分数傅里叶变换域进行了推广,更重要的是解决了其前述面临的问题。本文给出了相应的理论推导,并进行了仿真分析,仿真结果与理论分析一致。The classical Shannon sampling theorem has a profound influence on signal processing and communication. With the increasing contradiction between high rate sampling and conversion accuracy, the traditional analog to digital conversion technology, which is based on the Shannon sampling theorem, is facing a great challenge, especially for the bottleneck effect on reducing the sampling rate. In recent years, the analog-to-information conversion（AIC） technology, which is based on the theory of compressive sensing, provides an effective method to solve this problem. However, the signal model of the existing AIC is only suitable for sparse signals band-limited in the Fourier transform（FT） domain. It cannot be applied to non-bandlimited chirp signals which is widely used in electronic information systems, including radar and communications. Towards this end, we propose a new AIC based on the fractional Fourier transform（FRFT）, which is not only the extension of the traditional AIC in the FRFT domain, but also can solve the problem as mentioned above. The theoretical derivation is presented, and the corresponding simulation analysis is also given. The simulation results are consistent with the theoretical analysis.

关 键 词：分数阶傅里叶变换 随机解调 压缩感知 采样 

分 类 号：TN911.7[电子电信—通信与信息系统]