维格纳—威利分布与Radon-Wigner变换在信号时—频分析中的应用研究
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摘要
本文重点研究讨论了时-频分析法的基本理论及适用于时-频分析法的两个重要工具：维格纳-威利分布和Radon-Wigner变换，并实现了它们在地震信号处理中的初步应用。处理结果表明，对于单分量信号维格纳-威利分布具有良好的时-频聚集性，因此它对于单分量信号的处理具有很好的效果；而对于多分量信号由于交叉项的存在使得维格纳-威利分布不再很有效，有时甚至会由于交叉项的严重干扰使得信号项变得完全无法分辨。另外，维格纳-威利分布是完全有噪的，但它对噪声是不敏感的，因此可以利用维格纳-威利分布实现对含噪信号的去噪处理。理论上线性调频信号的Radon-Wigner变换在Radon-Wigner平面上以尖峰形式表现，因此Radon-Wigner变换能够有效描述线性调频信号的物理特征，抑制在维格纳-威利分布中产生的交叉项。在Radon-Wigner平面中随机噪声是呈点状随机散布开的，因此利用Radon-Wigner变换还能对含噪线性调频信号进行去噪处理。
The paper discusses mainly the essential theory of time-frequency analysis method and two important tools: Wigner - Ville distribution , Radon - Wigner transform that applies to the time-frequency analysis method. And it validates that they can applies to the semic signals processing. The processing result indicates that Wigner - Ville distribution has well time-frequency collective feature for single component signal,it applies to single component signal processing. However, Wigner - Ville distribution isn't enough effective applied to multicomponent signals processing for existing crossed items ,sometimes signal items completely can't be distinguished from distribution for serious disturbance of crossed items.In addition,we can utilize the Wigner - Ville distribution to reduce the random noise of signals in that Wigner - Ville distribution isn't enough sensitive to noise.In theory, Radon - Wigner transform of LFM signals produces a distinct maxima(peak) in the Radon-Wigner plane, so it describe effectively the feature of the LFM signals and suppress effectively the crossed items along with Wigner - Ville distribution.we can utilize the Radon - Wigner transform to reduce the random noise of LFM signals in that the noise distrbute as dot at random in the Radon - Wigner plane.
The paper discusses mainly the essential theory of time-frequency analysis method and two important tools: Wigner - Ville distribution , Radon - Wigner transform that applies to the time-frequency analysis method. And it validates that they can applies to the semic signals processing. The processing result indicates that Wigner - Ville distribution has well time-frequency collective feature for single component signal,it applies to single component signal processing. However, Wigner - Ville distribution isn't enough effective applied to multicomponent signals processing for existing crossed items ,sometimes signal items completely can't be distinguished from distribution for serious disturbance of crossed items.In addition,we can utilize the Wigner - Ville distribution to reduce the random noise of signals in that Wigner - Ville distribution isn't enough sensitive to noise.In theory, Radon - Wigner transform of LFM signals produces a distinct maxima(peak) in the Radon-Wigner plane, so it describe effectively the feature of the LFM signals and suppress effectively the crossed items along with Wigner - Ville distribution.we can utilize the Radon - Wigner transform to reduce the random noise of LFM signals in that the noise distrbute as dot at random in the Radon - Wigner plane.
引文
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[32] Chase M K. Radom noise reduction by 3-D spatial prediction filtering. 62nd Ann Internat Mtg, Expanded Abstracts. 1992,1152-1153.
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[37] Barbarossa S. Analysis of multicomponent LFM signals by a combined Wigner-Hough
transform. IEEE Trans. Signal Processing, 1995,43:1511-1515.
[38] Kohlmann K. Corner detection in natural images based on the 2-D Hilbert transform. Signal Procesing, 1996,48:225-234.
[39] 段雪江等，多分量信号的最优时频表示。信号处理，1996，Vol．12，No．3，280-284．
[40] 王文华、王宏禹等，非平稳信号的一种ARMA模型参数估计法。信号处理，1998，Vol．14．No．1，33-37．
[41] 王忠仁等，三维叠后随机噪声衰减技术。石油物探，1999，Vol．38，No．4，31-35．
[42] 高千里等，反混叠离散时间时频颁布。北京大学学报(自然科学版)，1999，Vol．35，No．1，112-118．
[2] (美)奥本海姆著，董士嘉等译，数字信号处理。北京：科学出版社，1980．
[3] 贾毓聪等译，连续信号、离散信号与系统分析。人民教育出版社，1983．
[4] 黄世霖，工程信号处理。人民交通出版社，1984．
[5] 何樵登，地震勘探原理与方法。北京：地质出版社，1986．
[6] 吴宣志；等，富里叶变换和位场谱分析方法及其应用。测绘出版社，1987．
[7] 冯德益，地震波理论与应用。北京：地震出版社，1988．
[8] 宗孔德，数字信号处理。北京，清华大学出版社，1990．
[9] 李衍达，信号重构理论及其应用。清华大学出版社，1991．
[10] (美)达吉恩著，程佩青，冯一云译，多维数字信号处理。科学出版社，1991．
[11] 王宝祥，信号与系统。哈尔滨工业大学出版社，1992．
[12] 张公礼等，数学谱方法的理论与应用。北京：国防工业出版社，1992．
[13] 赵鸿儒等，工程多波地震勘探。北京：地质出版社，1992．
[14] 陈行禄等，信号分析与处理。北京航空航天大学出版社，1993．
[15] 黄建国等人译，现代谱估计原理与应用。北京：科学出版社，1994．
[16] 李世华等，物探数据处理。北京：地质出版社，1995．
[17] 吴湘淇，信号、系统与信号处理(上、下)。电子工业出版社，1996．
[18] 徐伯勋等，信号处理及应用。北京：地质出版社，1997．
[19] 张贤达，信号处理中的线性代数。北京：科学出版社，1997．
[20] 张贤达，现代信号处理。北京：清华大学出版社，1999．
[21] 毛用才等，随机过程。西安电子科技大学出版社，1999．
[22] 张贤达等，非平稳信号分析与处理。北京：国防工业出版社，1999．
[23] 赵淑清等，随机信号分析。哈尔滨：哈尔滨工业出版社，1999．
[24] 王宏禹，非平稳随机信号分析与处理。北京：国防工业出版社，1999．
[25] 刘财等，地球物理场中近代数学方法。长春：吉林科学技术出版社，1999．
[26] 王宏禹，邱天爽，自适应噪声抵消与时间延迟估计。大连理工大学出版社，1999．
[27] 白居宪译，时一频分析：理论与应用。西安交通大学出版社，2000．
[28] 邹谋炎，反卷积和信号复原。国防工业出版社，2000．
[29] 张其善，金明录，信号复制生成理论及应用。人民邮电出版社，2001．
[30] Canals L L. Random noise reduction. Expanded Abstracts of the 54th Annual SEG Meeting. 1984,525-527.
[31] J.C. Wood and D.T. Barry, Radon transformation of the Wigner spectrum, Proc. SPIE:Advanced Architectures, Algorithms for Signal Processing, 1992,1770:358-375.
[32] Chase M K. Radom noise reduction by 3-D spatial prediction filtering. 62nd Ann Internat Mtg, Expanded Abstracts. 1992,1152-1153.
[33] Wood J C, Barry D T. Linear signal synthesis using the Radon-Wigner transform. IEEE Trans. Signal Processing, 1994,42:2105-2111.
[34] John C. Wood and Daniel T. Barry, Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linerar-FM signals. IEEE Trans. Signal Processing, 1994,42:2094-2104.
[35] Hlawatsch F, Kozek W. Time-frequency projection filters and time- frequency signal expansions IEEE. Trans. Signal Processing, 1994,42:3321-3334.
[36] Abma R and Clearbout J. Lateral prediction for noise attenution by t-x and f-x techniques. Geophysics, 1995,60(6):1887-1896.
[37] Barbarossa S. Analysis of multicomponent LFM signals by a combined Wigner-Hough
transform. IEEE Trans. Signal Processing, 1995,43:1511-1515.
[38] Kohlmann K. Corner detection in natural images based on the 2-D Hilbert transform. Signal Procesing, 1996,48:225-234.
[39] 段雪江等，多分量信号的最优时频表示。信号处理，1996，Vol．12，No．3，280-284．
[40] 王文华、王宏禹等，非平稳信号的一种ARMA模型参数估计法。信号处理，1998，Vol．14．No．1，33-37．
[41] 王忠仁等，三维叠后随机噪声衰减技术。石油物探，1999，Vol．38，No．4，31-35．
[42] 高千里等，反混叠离散时间时频颁布。北京大学学报(自然科学版)，1999，Vol．35，No．1，112-118．