时频分析方法：研究与展望
Time-Frequency Analysis Method: Research and Prospect
DOI: 10.12677/JISP.2018.71003, PDF,  被引量   
作者: 武国宁*, 齐晶晶：中国石油大学(北京)，理学院数学系，北京；周亚同：河北工业大学，电子信息工程学院，天津
关键词: 时频分析；非稳态信号；频谱分析；Time-Frequency Analysis； Non-Stationary Signal； Spectral Analysis
摘要: 时频分析联合时间频率表示一维时间信号，是非稳态信号处理的重要工具之一。本文综述了时频分析方法的研究进展，在此基础上阐述了各种时频分析方法的原理及其优缺点。通过数值模拟试验，比较了各种时频分析方法的频谱表示特征。最后，对时频分析方法进行了展望。
Abstract: Time-frequency analysis method represents one-dimensional time signal into time and frequency domains, which is an important tool for non-stationary signal analysis. In this paper, the time-frequency analysis methods were reviewed; furthermore, a survey of the principles, the ad-vantages and disadvantages of various time-frequency methods were given. Numerical simulations were carried out for comparisons. Finally, a short prospection about time-frequency analysis was given in this paper.
文章引用：武国宁, 齐晶晶, 周亚同. 时频分析方法：研究与展望[J]. 图像与信号处理, 2018, 7(1): 24-35. https://doi.org/10.12677/JISP.2018.71003

参考文献

[1] Tary, J.B., Herrera, R.H., et al. (2014) Spectral Estimation—What Is New? What Is Next? Reviews of Geophysics, 52, 723-749. [Google Scholar] [CrossRef] 
[2] Han, L., Sacchi, M.D., et al. (2014) Spectral Decomposition and De-Noising via Time-Frequency and Space-Wave- number Reassignment. Geophysical Prospecting, 62, 244-257. [Google Scholar] [CrossRef] 
[3] Han, J. and Van der Baan, M. (2013) Empirical Mode Decomposition for Seismic Time-Frequency Analysis. Geophysics, 78, O9-O19. [Google Scholar] [CrossRef] 
[4] Allen. J.B. (1977) Short Time Spectral Analysis, Synthesis, and Modification by Discrete Fourier Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, 25, 235-238. [Google Scholar] [CrossRef] 
[5] Morlet, J., Arens, G., Fourgeau, E., et al. (1982) Wave Propagation and Sampling Theory—Part I: Complex Signal and Scattering in Multilayered Media. Geophysics, 47, 203-221. [Google Scholar] [CrossRef] 
[6] Stockwell, R.G., Mansinha, L. and Lowe, R.P. (1996) Localization of the Complex Spectrum: The S Transform. IEEE Transactions on Signal Processing, 44, 998-1001. [Google Scholar] [CrossRef] 
[7] Wigner, E.P. (1932) On the Quantum Correction for Thermodynamic Equilibrium. Physical Review, 40, 749-759. [Google Scholar] [CrossRef] 
[8] Ville, J. (1948) Theorie et applications de la notion de signal analytique. Calbes et Transmission, 2A, 61-74.
[9] Andrieux, J C., Feix, M.R., Mourgues, G., et al. (1987) Optimum Smoothing of the Wigner-Ville Distribution. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35, 764-769. [Google Scholar] [CrossRef] 
[10] Choi, H.I. and Williams, W.J. (1989) Improved Time-Frequency Represen-tation of Multicomponent Signals Using Exponential Kernels. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37, 862-871. [Google Scholar] [CrossRef] 
[11] Baraniuk, R.G. and Jones, D.L. (1993) Signal-Dependent Time-Frequency Analysis Using Radially Gaussian Kernel. Signal Processing, 32, 263-284. [Google Scholar] [CrossRef] 
[12] Chen, S.S., Donoho, D.L. and Saunders, M.A. (2001) Atomic Decomposi-tion by Basis Pursuit. Siam Review, 43, 129-159. [Google Scholar] [CrossRef] 
[13] Auger, F., Hilairet, M., Guerrero, J.M., et al. (2013) Industrial Applications of the Kalman Filter: A Review. IEEE Transactions on Industrial Electronics, 60, 5458-5471. [Google Scholar] [CrossRef] 
[14] Huang, N.E., Shen, Z., Long, S.R., et al. (1998) The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis. The Royal Society, 454, 903-995. [Google Scholar] [CrossRef] 
[15] Daubechies, I., Lu, J.F. and Wu, H.-T. (2011) Synchrosqueezed Wavelet Transforms: A Tool for Empirical Mode Decomposition. Applied and Computational Harmonic Analysis, 30, 243-261. [Google Scholar] [CrossRef] 
[16] Daubechies, I. (1990) The Wavelet Transform, Time-Frequency Localization and Signal Analysis. IEEE Transactions on Information Theory, 36, 961-1005. [Google Scholar] [CrossRef] 
[17] Cohen, L. (1995) Time-Frequency Analysis: Theory and Applications. Prentice Hall, Upper Saddle River.
[18] Wu, Z. and Huang, N.E. (2009) Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method. Advances in Adaptive Data Analysis, 1, 1-41. [Google Scholar] [CrossRef] 
[19] Torres, M.E., Colominas, M.A., et al. (2011) A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise. IEEE International Conference on Acoustics, Speech and Signal Processing, Prague, 22-27 May 2011, Vol. 125, 4144-4147. [Google Scholar] [CrossRef] 
[20] Auger, F. and Flandrin, P. (2013) Time-Frequency Reassignment and Synchrosqueezing: An Overview. IEEE Signal Processing Magazine, 30, 32-41. [Google Scholar] [CrossRef] 
[21] Mallat, S.G. and Zhang, Z. (1993) Matching Pursuits with Time-Frequency Dictionaries. IEEE Transactions on Signal Processing, 41, 3397-3415. [Google Scholar] [CrossRef] 
[22] Friedman, J.H. and Stuetzle, W. (1981) Projection Pursuit Regression. Journal of the American Statistical Association, 76, 817-823. [Google Scholar] [CrossRef] 
[23] Fildes, R. (1991) Forecasting, Structural Time Series Models and the Kalman Filter: Bayesian Forecasting and Dynamic Models. Journal of the Operational Research Society, 42, 1031-1033. [Google Scholar] [CrossRef] 
[24] Hlawatsch, F. and Boudreaux-Bartels, G.F. (1992) Linear and Quadratic Time-Frequency Signal Representations. IEEE Signal Processing Magazine, 9, 21-67. [Google Scholar] [CrossRef] 
[25] Claasen, T.A.C.M. and Mecklenbrauker, W. (1980) The Wigner Distribution—A Tool for Time-Frequency Signal Analysis. Part I: Continuous Time Signals. Philips Journal of Research, 35, 217-250.
[26] Claasen, T.A.C.M. and Mecklenbrauker, W. (1980) The Wigner Distribution—A Tool for Time-Frequency Signal Analysis. Part II: Discrete Time Signals. Philips Journal of Research, 35, 276-250.
[27] Claasen, T.A.C.M. and Mecklenbrauker, W. (1980) The Wigner Distribution—A Tool for Time-Frequency Signal Analysis. Part II: Relations with Other Time-Frequency Signal Transformations. Journal of Research, 35, 372-389.
[28] Cohen, L. (1989) Time-Frequency Distributions a Reviews. Proceedings of the IEEE, 77, 941-981. [Google Scholar] [CrossRef] 
[29] Flandrin, P. and Goncalves, P. (1996) Geometry of Affine Time-Frequency Distributions. Applied & Computational Harmonic Analysis, 3, 10-39. [Google Scholar] [CrossRef] 
[30] Jones, D.L. and Baraniuk, R.G. (1995) An Adaptive Optimal-Kernel Time-Frequency Representation. IEEE Transactions on Signal Processing, 43, 2361-2371. [Google Scholar] [CrossRef] 
[31] Auger, F. and Flandrin, P. (1995) Improving the Readability of Time-Frequency and Time-Scale Representations by the Reassignment Method. IEEE Transactions on Signal Processing, 43, 1068-1089. [Google Scholar] [CrossRef] 
[32] Jokanovic, B. and Amin, M. (2015) Reduced Interference Sparse Time-Frequency Dis-tributions for Compressed Observations. IEEE Transactions on Signal Processing, 63, 6698-6709. [Google Scholar] [CrossRef] 
[33] 郑近德, 潘海洋, 程军圣. 非平稳信号分析的广义解析模态分解方法[J]. 电子学报, 2016, 44(6): 1458-1464.
[34] 行鸿彦, 朱清清. 基于集成经验模态分解的海杂波去噪[J]. 电子学报, 2016, 44(1): 1-7.
[35] 胡爱军, 孙敬敬, 向玲. 经验模态分解中的模态混叠问题[J]. 振动、测试与诊断, 2011, 31(4): 429-434.
[36] 邓小军, 曹源, 张玉琢, 等. 改进希尔伯特-黄变换分析波磨对列车时频特征的影响[J]. 电子学报, 2016, 44(10): 2294-2299.
[37] Herrera, R.H., Han, J. and van der Baan, M. (2014) Applications of the Synchrosqueezing Transform in Seismic Time-Frequency Analysis. Geophysics, 79, V55-V64. [Google Scholar] [CrossRef] 
[38] Li, C. and Liang, M. (2012) A Generalized Synchrosqueezing Transform for Enhancing Signal Time-Frequency Representation. Signal Processing, 92, 2264-2274. [Google Scholar] [CrossRef] 
[39] Daubechies, I. (1996) A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models. In: Aldroubi, A. and Unser, M., Eds., Wavelets in Medicine & Biology, CRC Press, Boca Raton, 527-546.
[40] Huang, Z., Zhang, J., Zhao, T., et al. (2016) Synchrosqueezing S-Transform and Its Application in Seismic Spectral Decomposition. IEEE Transactions on Geoscience and Remote Sensing, 54, 817-825. [Google Scholar] [CrossRef] 
[41] 芮国胜, 王林, 田文飚. 一种基于基追踪压缩感知信号重构的改进算法[J]. 电子测量技术, 2010, 33(4): 38-41.
[42] Rioul, O. and Vetterli, M. (1991) Wavelets and Signal Processing. IEEE Signal Processing Magazine, 8, 14-38. [Google Scholar] [CrossRef] 
[43] Feng, Z., Liang, M. and Chu, F. (2013) Recent Advances in Time-Frequency Analysis Methods for Machinery Fault Diagnosis: A Review with Application Examples. Mechanical Systems and Signal Processing, 38, 165-205. [Google Scholar] [CrossRef] 
[44] Tropp, J.A. and Wright, S.J. (2009) Computational Methods for Sparse Solu-tion of Linear Inverse Problems. Proceedings of the IEEE, 98, 948-958. [Google Scholar] [CrossRef] 
[45] Figueiredo, M.A.T., Nowak, R.D. and Wright, S.J. (2007) Gradient Projec-tion for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. IEEE Journal of Selected Topics in Signal Processing, 1, 586-597. [Google Scholar] [CrossRef] 
[46] Bergeaud, F. and Mallat, S. (1998) Matching Pursuit of Images. Wavelet Analysis and Its Applications, 7, 285-300. [Google Scholar] [CrossRef]