| 稀疏傅里叶变换理论及研究进展 |
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| 引用本文： | 仲顺安,王雄,王卫江,刘箭言.稀疏傅里叶变换理论及研究进展[J].北京理工大学学报,2017,37(2):111-118. |
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| 作者姓名： | 仲顺安 王雄 王卫江 刘箭言 |
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| 作者单位： | 北京理工大学信息与电子学院,北京,100081;北京理工大学信息与电子学院,北京100081;重庆通信学院信息工程系,重庆400035 |
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| 摘 要： | 稀疏傅里叶变换（sparse Fourier transform，SFT）是一种稀疏信号离散傅里叶变换的新算法，比传统快速傅里叶变换（fast Fourier transform，FFT）更加高效.综述了SFT的理论框架、约束条件及频谱重排、窗函数滤波、降采样FFT等关键技术问题，结合算法最新理论成果，归纳出4种不同的重构方法:哈希映射法、混叠同余法、相位解码法、二分查找法.最后介绍了SFT理论的应用成果，并展望了其未来可能的发展方向.
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| 关 键 词： | 稀疏傅里叶变换 频谱重排 平坦窗函数 降采样FFT 哈希映射 |
| 收稿时间： | 2014/11/6 0:00:00 |
Recent Advances in the Sparse Fourier Transform |
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| ZHONG Shun-an,WANG Xiong,WANG Wei-jiang and LIU Jian-yan.Recent Advances in the Sparse Fourier Transform[J].Journal of Beijing Institute of Technology(Natural Science Edition),2017,37(2):111-118. |
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| Authors: | ZHONG Shun-an WANG Xiong WANG Wei-jiang and LIU Jian-yan |
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| Institution: | 1. School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China;2. Department of Information Engineering, Chongqing Communication Institute, Chongqing 400035, China |
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| Abstract: | Sparse Fourier transform (SFT) is a novel algorithm for discreting Fourier transform (DFT) on sparse signals, and is more efficient than the traditional fast Fourier transform (FFT). Reviewing the theoretical framework, restrictions and the key technical problems such as random spectrum permutation, window filtering and subsampled FFT, our different kinds of reconstruction means:hash mapping, aliasing-based search, phase decoding, binary search were introduced based on the latest theoretical achievements of the algorithms. Finally, some applications based on SFT were introduced, and its outlooks were presented. |
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| Keywords: | SFT spectrum permutation flat window function subsampled FFT Hash function |
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