欠采样率下多频率成分的估计方法

高育兵; 梁 红; 杜金香

doi:10.11993/j.issn.1673-1948.2012.01.004

欠采样率下多频率成分的估计方法

doi: 10.11993/j.issn.1673-1948.2012.01.004

1.
海军装备部驻西安地区军事代表局, 陕西西安, 710054
2.
西北工业大学航海学院, 陕西西安, 710072

基金项目: 国家自然科学基金(60702067)

详细信息

作者简介:
高育兵(1964-), 男, 高级工程师, 研究方向为水声信号处理.

中图分类号: TJ630.34；TN911.7
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- 文章访问数: 928
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- 被引次数: 0
出版历程
- 收稿日期: 2011-04-11
- 修回日期: 2011-06-10
- 刊出日期: 2012-02-20

Multiple-Frequency Estimation Method with Undersampled Waveform

1.
XI′an Representative Bureau, Naval Armament Department, Xi′an 710054, China
2.
College of Marine Engineering, North-western Polytechnical University, Xi′an 710072, China

摘要

摘要: 针对信号处理和雷达系统中常见的信号频率大于采样频率或采样频率小于奈奎斯特情况下信号多个频率成分的估计问题, 提出了采用一组非互质的模数和相应的一组有误差的余数, 同时重构多个任意正实数的广义稳健中国剩余定理(GRCRT), 定理1首先给出了余数与重构的正实数的一一对应所需要满足的条件, 定理2 给出了重构正实数有唯一解的条件。将该定理用于欠采样下多个信号频率估计, 仿真实例验证了余数估计有误差时同时估计多个正实数算法的稳健性和实际工程应用前景。
- 广义稳健中国剩余定理 /
- 欠采样 /
- 多频率估计
Abstract: In some applications, such as signal processing and radar systems, it is preferred that the range of the fre-quencies is as large as possible for a given sampling rate and the sampling rate is below the Nyquist rate. In both cases, frequencies estimation from undersampled waveforms is necessary. In this paper, a generalized robust Chinese remain-der theorem (GRCRT) for reconstructing multiple positive real numbers is presented, where modules are not pair-wisely co-prime and the remainders with errors. In theorem 1, the sufficient condition for the multiple real numbers to satisfy is given, where all remainders have errors and we can determine which one in the remainder set is the remainder of any real number. And an approach to determine unique solution of multiple real numbers from the remainder set with errors is proposed in theorem 2. Simulation results show that the present method is efficient for estimating multiple frequencies from multiple undersampled waveforms with sampling rate below the Nyquist rate, and it can be applied to such areas as digital signal processing.
- generalized robust Chinese remainder theorem(GRCRT) /
- undersample /
- multiple-frequency estimation

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参考文献(9)

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