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基于中国余数定理的重构算法的信号频率估计是近年来信号处理、电磁学以及光学等领域的前沿问题，但目前这些研究仅限于对复指数信号做粗略频率估计. 因而，本文把基于中国余数定理的频率估计从复指数信号粗估计拓展到实余弦信号精细估计领域，其所提出的估计方案处理过程如下：1） 对高频余弦波形进行过零点检测，确定信号的相位信息；2） 对各路欠采样信号做快速傅里叶变换，并借助Candan估计器对各路谱峰值做频率校正以获取高精度余数估计，基于此算出频偏值以做相位校正；3）用提出的基于相位特征分类方法对校正得到的余数做筛选；4） 将筛选出的频率余数代入闭合形式的中国余数定理得到原信号频率的高精度估计. 此外，本文还推导出了频率估计方差的理论表达式. 数据模拟实验验证了该表达式的正确性，实验结果还反映了本文提出的方案具有高精度和高抗噪性能.Frequency estimation based on the reconstruction algorithm of the Chinese remainder theorem(CRT) is one of the frontier focuses in the fields of signal processing, electromagnetism, and optics etc. Howerver, the existing studies can only realize a rough frequency estimation of complex exponential signals. Hence this paper generalizes the CRT-based frequency reconstruction from a rough frequency estimation of complex exponential signals to the accurate frequency estimation of sinusoidal signals. The procedure of the proposed estimation scheme is as follows: (1) Detect zero crossing point on the original high-frequency sinusoidal waveform so as to determine the ideal phase information; (2) implement fast Fourier transform(FFT) to each path's undersampled signal, and then use Candan estimator to correct the frequencies at the peak FFT spectral bins so that the frequency biases can be extracted to realize phase correction; (3) use the proposed classification method based on phase features to screen the corrected remainders; (4)substitute the filtered frequency remainders into the closed-form robust Chinese remainder theorem to obtain the high-accuracy frequency estimation of the original signal. Additionally, this paper also deduces the theoretic expressions of the frequency estimation variance, which is also verified through numerical simulation. And the experimental results also reflect that the proposed scheme possesses high precision and high robustness to noise.
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Keywords:
- Chinese remainder theorem /
- undersampled /
- frequency estimation /
- remainder screening
[1] Xia X G, Liu K J 2005 IEEE Signal Processing Letters 12 768
[2] Chen Zh, Zeng Y Ch, Fu Zh J 2008 Acta Phys. Sin. 57 46(in Chinese) [陈争, 曾以成, 付志坚 2008 物理学报 57 46]
[3] Cong Ch, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301(in Chinese) [丛超, 李秀坤, 宋扬. 2014 物理学报 63 064301]
[4] Xia X G, Wang G Y 2007 IEEE Signal Processing Letters 14 247
[5] Li X W, Liang H, Xia X G 2009 IEEE Trans. Signal Process 57 4314
[6] Li X W, Xia X G 2008 IEEE Signal Processing Letters 15 665
[7] Qing H Y, Zhang Y N, Zhou Ch, Zhao Zh Y, Chen G 2014 Acta Phys. Sin. 63 094301(in Chinese) [青海银, 张援农, 周晨, 赵正予, 陈罡. 2014 物理学报 63 094301]
[8] Cheng F, Wang Y Z 2012 Chin. Phys. B. 21 070309
[9] Bai Y F, Zhai Sh Q, Gao J R, Zhang J X 2011 Chin. Phys. B 20 034207
[10] Mcclellen J H, Rader C M 1979 Number Theory in Digital Signal Processing (Englewood Cliffs, NJ: Prentice-Hall)
[11] Ding C, Pei D, Salomaa A 1996 Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography (Singapore: World Scientific Publishing Co. Pte. Ltd.) p24
[12] Goldreich O, Ron D, Sudan M 2000 IEEE Trans. Inf. Theory 46 1330
[13] Guruswami V, Sahai A, Sudan M 2000 Proceedings 41st Annual Symposium on Foundations of Computer Science Redondo Beach, CA, Nov 12-14, 2000 p159
[14] Li G, Meng H D, Xia X G, Peng Y N 2008 Sensors 8 1343
[15] Li X W, Xia X G 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP) Dallas, TX, March 14-19, 2010 p2810
[16] Wang W J, Xia X G 2010 IEEE Transactions on Signal Processing 58 5655
[17] Candan C 2011 IEEE Signal Processing Letters 18 351
[18] Candan C 2013 IEEE Signal Processing Letters 20 913
[19] Quinn B G 1994 IEEE Transactions on Signal Processing 42 1264
[20] Macleod M D 1998 IEEE Transactions on Signal Processing 46 141
[21] Jacobsen E, Kootsookos P 2007 IEEE Signal Process. Mag 24 123
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[1] Xia X G, Liu K J 2005 IEEE Signal Processing Letters 12 768
[2] Chen Zh, Zeng Y Ch, Fu Zh J 2008 Acta Phys. Sin. 57 46(in Chinese) [陈争, 曾以成, 付志坚 2008 物理学报 57 46]
[3] Cong Ch, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301(in Chinese) [丛超, 李秀坤, 宋扬. 2014 物理学报 63 064301]
[4] Xia X G, Wang G Y 2007 IEEE Signal Processing Letters 14 247
[5] Li X W, Liang H, Xia X G 2009 IEEE Trans. Signal Process 57 4314
[6] Li X W, Xia X G 2008 IEEE Signal Processing Letters 15 665
[7] Qing H Y, Zhang Y N, Zhou Ch, Zhao Zh Y, Chen G 2014 Acta Phys. Sin. 63 094301(in Chinese) [青海银, 张援农, 周晨, 赵正予, 陈罡. 2014 物理学报 63 094301]
[8] Cheng F, Wang Y Z 2012 Chin. Phys. B. 21 070309
[9] Bai Y F, Zhai Sh Q, Gao J R, Zhang J X 2011 Chin. Phys. B 20 034207
[10] Mcclellen J H, Rader C M 1979 Number Theory in Digital Signal Processing (Englewood Cliffs, NJ: Prentice-Hall)
[11] Ding C, Pei D, Salomaa A 1996 Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography (Singapore: World Scientific Publishing Co. Pte. Ltd.) p24
[12] Goldreich O, Ron D, Sudan M 2000 IEEE Trans. Inf. Theory 46 1330
[13] Guruswami V, Sahai A, Sudan M 2000 Proceedings 41st Annual Symposium on Foundations of Computer Science Redondo Beach, CA, Nov 12-14, 2000 p159
[14] Li G, Meng H D, Xia X G, Peng Y N 2008 Sensors 8 1343
[15] Li X W, Xia X G 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP) Dallas, TX, March 14-19, 2010 p2810
[16] Wang W J, Xia X G 2010 IEEE Transactions on Signal Processing 58 5655
[17] Candan C 2011 IEEE Signal Processing Letters 18 351
[18] Candan C 2013 IEEE Signal Processing Letters 20 913
[19] Quinn B G 1994 IEEE Transactions on Signal Processing 42 1264
[20] Macleod M D 1998 IEEE Transactions on Signal Processing 46 141
[21] Jacobsen E, Kootsookos P 2007 IEEE Signal Process. Mag 24 123
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