Study on High Efficient Algorithm for Cyclic Correntropy Spectral Analysis
-
摘要: 针对循环相关熵谱估计循环周期图检测(CPD)算法存在计算效率低、频谱分辨率低和易产生“频谱泄漏”的问题，该文提出一种循环相关熵谱估计的Correntrogram算法。Correntrogram算法借鉴Wigner-Ville 分布(WVD)时频分辨率高的优势，将WVD算法中瞬时自相关函数替换为时变自相关熵函数，即可得到一种循环相关熵谱密度估计算法，称为Correntrogram。首先计算信号的时变自相关熵函数矩阵，再计算时变自相关熵函数矩阵各行的FFT，得到循环自相关熵函数矩阵，最后计算循环自相关熵函数矩阵各列的FFT，得到循环相关熵谱密度。通过仿真调幅信号的处理结果证明：Correntrogram算法有效提高了循环相关熵谱估计效率，避免了“频谱泄漏”，提高了频谱分辨率，该算法程序运行可靠。Abstract: A high computationally efficient algorithm for cyclic correntropy spectral analysis is presented which is named as Correntrogram algorithm. Correntrogram algorithm overcomes the problems of Cyclic Periodogram Detection (CPD) method, such as high computational cost, low resolution and spectrum leakage. Correntrogram utilizes the advantages of Wigner-Ville Distribution (WVD) which has high time frequency resolution. By replacing the time-varying autocorrelation function with the time-varying auto-correntropy function in the WVD algorithm, the cyclic auto-correntropy spectral density estimation algorithm can be realized. First, the time-varying auto-correntropy function matrix of the signal is calculated, and then the Fast Fourier Transform (FFT) of each row of the time-varying auto-correntropy function matrix is computed to get the cyclic auto-correntropy function matrix. Finally, the FFT of each column of the cyclic auto-correntropy function matrix is calculated to get the cyclic auto-correntropy spectral density function. The validity of the proposed estimator is demonstrated on a simulative amplitude modulation signal. The simulative result shows that not only the proposed estimator is computationally efficient, but also has high frequency resolution and overcomes the spectrum leakage. The performance of Correntrogram is better than that of CPD method.
-
GARDNER W A. The spectral correlation theory of cyclostationary time-series[J]. Signal Processing, 1986, 11(1): 13–36. doi: 10.1016/0165-1684(86)90092-7 GARDNER W A, NAPOLITANO A, and PAURA L. Cyclostationarity: Half a century of research[J]. Signal Processing, 2006, 86(4): 639–697. doi: 10.1016/j.sigpro.2005.06.016 NAPOLITANO A. Cyclostationarity: Limits and generalizations[J]. Signal Processing, 2016, 120: 323–347. doi: 10.1016/j.sigpro.2015.09.013 NAPOLITANO A. Cyclostationarity: New trends and applications[J]. Signal Processing, 2016, 120: 385–408. doi: 10.1016/j.sigpro.2015.09.011 GARDNER W A and SPOONER C M. Signal interception: Performance advantages of cyclic-feature detectors[J]. IEEE Transactions on Communications, 1992, 40(1): 149–159. doi: 10.1109/26.126716 GARDNER W A and SPOONER C M. Detection and source location of weak cyclostationary signals: Simplifications of the maximum-likelihood receiver[J]. IEEE Transactions on Communications, 1993, 41(6): 905–916. doi: 10.1109/26.231913 GELLI G, IZZO L, and PAURA L. Cyclostationarity-based signal detection and source location in non-Gaussian noise[J]. IEEE Transactions on Communications, 1996, 44(3): 368–376. doi: 10.1109/26.486331 BOUILLAUT L and SIDAHMED M. Cyclostationary approach and bilinear approach: Comparison, applications to early diagnosis for helicopter gearbox and classification method based on HOCS[J]. Mechanical Systems and Signal Processing, 2001, 15(5): 923–943. doi: 10.1006/mssp.2001.1412 ANTONIADIS I and GLOSSIOTIS G. Cyclostationary analysis of rolling-element bearing vibration signals[J]. Journal of Sound and Vibration, 2001, 248(5): 829–845. doi: 10.1006/jsvi.2001.3815 邱天爽. 相关熵与循环相关熵信号处理研究进展[J]. 电子与信息学报, 2020, 42(1): 105–118. doi: 10.11999/JEIT190646QIU Tianshuang. Development in signal processing based on correntropy and cyclic correntropy[J]. Journal of Electronics &Information Technology, 2020, 42(1): 105–118. doi: 10.11999/JEIT190646 郭莹, 邱天爽. 基于分数低阶统计量的盲多用户检测算法[J]. 电子学报, 2007, 35(9): 1670–1674. doi: 10.3321/j.issn:0372-2112.2007.09.011GUO Ying and QIU Tianshuang. Blind multiuser detector based on FLOS in impulse noise environment[J]. Acta Electronica Sinica, 2007, 35(9): 1670–1674. doi: 10.3321/j.issn:0372-2112.2007.09.011 MA Xinyu and NIKIAS C L. Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics[J]. IEEE Transactions on Signal Processing, 1996, 44(11): 2669–2687. doi: 10.1109/78.542175 邱天爽, 王宏禹, 孙永梅. 一种基于分数低阶协方差的自适应EP潜伏期变化检测方法[J]. 电子学报, 2004, 32(1): 91–95. doi: 10.3321/j.issn:0372-2112.2004.01.022QIU Tianshuang, WANG Hongyu, and SUN Yongmei. A fractional lower-order covariance based adaptive latency change detection for Evoked Potentials[J]. Acta Electronica Sinica, 2004, 32(1): 91–95. doi: 10.3321/j.issn:0372-2112.2004.01.022 李辉. 基于分数低阶统计量的频谱分析方法[J]. 天津职业技术师范大学学报, 2019, 29(2): 1–6, 18. doi: 10.19573/j.issn2095-0926.201902001LI Hui. Spectrum analysis based on fractional lower order statistics[J]. Journal of Tianjin University of Technology and Education, 2019, 29(2): 1–6, 18. doi: 10.19573/j.issn2095-0926.201902001 宋爱民, 邱天爽, 佟祉谏. 对称稳定分布的相关熵及其在时间延迟估计上的应用[J]. 电子与信息学报, 2011, 33(2): 494–498. doi: 10.3724/SP.J.1146.2010.00309SONG Aimin, QIU Tianshuang, and TONG Zhijian. Correntropy of the symmetric stable distribution and its application to the time delay estimation[J]. Journal of Electronics &Information Technology, 2011, 33(2): 494–498. doi: 10.3724/SP.J.1146.2010.00309 王鹏, 邱天爽, 任福全, 等. 对称稳定分布噪声下基于广义相关熵的DOA估计新方法[J]. 电子与信息学报, 2016, 38(8): 2007–2013. doi: 10.11999/JEIT151217WANG Peng, QIU Tianshuang, REN Fuquan, et al. A novel generalized correntropy based method for direction of arrival estimation in symmetric alpha stable noise environments[J]. Journal of Electronics &Information Technology, 2016, 38(8): 2007–2013. doi: 10.11999/JEIT151217 YU Ling, QIU Tianshuang, and LUAN Shengyang. Fractional time delay estimation algorithm based on the maximum correntropy criterion and the Lagrange FDF[J]. Signal Processing, 2015, 111: 222–229. doi: 10.1016/j.sigpro.2014.12.018 吴超, 李雅倩, 张亚茹, 等. 用于表示级特征融合与分类的相关熵融合极限学习机[J]. 电子与信息学报, 2020, 42(2): 386–393. doi: 10.11999/JEIT190186WU Chao, LI Yaqian, ZHANG Yaru, et al. Correntropy-based fusion extreme learning machine for representation level feature fusion and classification[J]. Journal of Electronics &Information Technology, 2020, 42(2): 386–393. doi: 10.11999/JEIT190186 LUAN Shengyang, QIU Tianshuang, ZHU Yongjie, et al. Cyclic correntropy and its spectrum in frequency estimation in the presence of impulsive noise[J]. Signal Processing, 2016, 120: 503–508. doi: 10.1016/j.sigpro.2015.09.023 FONTES A I R, REGO J B A, MARTINS A D M, et al. Cyclostationary correntropy: Definition and applications[J]. Expert Systems with Applications, 2017, 69: 110–117. doi: 10.1016/j.eswa.2016.10.029 LIU Tao, QIU Tianshuang, and LUAN Shengyang. Cyclic correntropy: Foundations and theories[J]. IEEE Access, 2018, 6: 34659–34669. doi: 10.1109/ACCESS.2018.2847346 ROBERTS R S, BROWN W A, and LOOMIS H H. Computationally efficient algorithms for cyclic spectral analysis[J]. IEEE Signal Processing Magazine, 1991, 8(2): 38–49. doi: 10.1109/79.81008 ANTONI J. Cyclic spectral analysis in practice[J]. Mechanical Systems and Signal Processing, 2007, 21(2): 597–630. doi: 10.1016/j.ymssp.2006.08.007 ANTONI J, XIN Ge, and HAMZAOUI N. Fast computation of the spectral correlation[J]. Mechanical Systems and Signal Processing, 2017, 92: 248–277. doi: 10.1016/j.ymssp.2017.01.011 LIU Weifeng, POKHAREL P P, and PRINCIPE J C. Correntropy: A localized similarity measure[C]. The 2006 IEEE International Joint Conference on Neural Network Proceedings, Vancouver, Canada, 2006: 4919–4924. doi: 10.1109/IJCNN.2006.247192. SANTAMARIA I, POKHAREL P P, and PRINCIPE J C. Generalized correlation function: Definition, properties, and application to blind equalization[J]. IEEE Transactions on Signal Processing, 2006, 54(6): 2187–2197. doi: 10.1109/TSP.2006.872524 LIU Weifang, POKHAREL P P, and PRINCIPE J C. Correntropy: Properties and applications in non-gaussian signal processing[J]. IEEE Transactions on Signal Processing, 2007, 55(11): 5286–5298. doi: 10.1109/tsp.2007.896065 GUNDUZ A and PRINCIPE J C. Correntropy as a novel measure for nonlinearity tests[J]. Signal Processing, 2009, 89(1): 14–23. doi: 10.1016/j.sigpro.2008.07.005 LI Hui, ZHENG Haiqi, and TANG Liwei. Wigner-ville distribution based on EMD for faults diagnosis of bearing[C]. The 3rd International Conference on Fuzzy Systems and Knowledge Discovery, Xi’an, China, 2006: 803–812. doi: 10.1007/11881599_99. -
下载:
图(17)
计量
- 文章访问数: 847
- HTML全文浏览量: 605
- PDF下载量: 85
- 被引次数: 0
下载:
