稀疏信号欠 Nyq uist采样与重构研究现状分析

摘要

传统的信号采样理论要求采样频率需高于Nyquist频率（信号最高频率）的两倍，给射频及超宽带领域的信号采样、存储和传输造成巨大压力。近年来针对可以进行稀疏表示的信号，欠Nyquist采样技术取得了很大的发展，大大降低了精确重构原始信号所需的采样率。综述性地归纳了目前可以进行欠Nyquist采样的信号模型，将出现的各种欠Nyquist采样总结为一个基本模型，并针对频域稀疏和时域稀疏信号分别对采样模型及原理进行了阐述，分析了采样信号的子空间探测和重建方法，讨论了稀疏信号欠Nyquist采样与重构的实现与应用现状，并对研究前景进行了展望。%Traditional signal sampling theories require a sampling rate than two times of Nyquist rate (the highest frequency of signals),greatly restrict the sampling,storage and transition of RF and super wideband signals.Resent years sub-Nyquist sampling achieved significant development on signal able to be represented sparsely,greatly reducing the sampling rate re-quired for perfectly recovery of the original signals.This paper generalized the signal models which satisfied the condition for sub-Nyquist sampling and summarized the several sub-Nyquist sampling frame into a basic model,respectively described the special model and principle aiming at frequency and time sparse signal.Then the paper analyzed the signal subspace detection and reconstruction methods and discussed the realization and implementation.At last,it prospected the research potentiality.