基于能量归一化窗的S变换及应用
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摘要
为了克服标准S变换对时频谱能量的"加权效应",构造了一种归一化窗S变换。它的窗函数满足能量归一化条件,减少了对高频分量的加权效应,而且可通过参数调整窗函数时宽。文中推导了归一化窗S正反变换的运算实现。模型信号的分析表明,归一化窗S变换在不损失时频分辨率的前提下,更能客观地反映非平稳信号中不同频率成分的能量分布特征,并可通过参数调整其时频分辨率。对实际地震信号的分析发现,它能更加真实地描述实际地震信号的高频衰减现象。
In order to avoid the "weighting effect" of the existing S transform(ST) suffered from the time-frequency spectral energy,a normalized window based S transform(NWST) is presented.The window function of NWST possesses the normalized energy and reduces the "weighting effect" for spectral energy at the higher frequency.The temporal width of NWST window can be adjusted by an additional parameter.Numerical implementation of NWST and its inverse transform are introduced.Simulation results of several signal models demonstrate that NWST can reflect the spectral energy distribution of different frequency components while maintaining the good time-frequency resolution.In addition,the time-frequency resolution of NWST can be further adjusted by the parameter.NWST is applied in the real seismic signal analysis.Results show that NWST can detect the high frequency attenuation of seismic signal using ST.
In order to avoid the "weighting effect" of the existing S transform(ST) suffered from the time-frequency spectral energy,a normalized window based S transform(NWST) is presented.The window function of NWST possesses the normalized energy and reduces the "weighting effect" for spectral energy at the higher frequency.The temporal width of NWST window can be adjusted by an additional parameter.Numerical implementation of NWST and its inverse transform are introduced.Simulation results of several signal models demonstrate that NWST can reflect the spectral energy distribution of different frequency components while maintaining the good time-frequency resolution.In addition,the time-frequency resolution of NWST can be further adjusted by the parameter.NWST is applied in the real seismic signal analysis.Results show that NWST can detect the high frequency attenuation of seismic signal using ST.
引文
[1]张贤达.现代信号处理[M].北京:清华大学出版社,2002:349-353.
[2]Stockwell R G,Mansinha L,Lowe R P.Localiza-tion of the complex spectrum:the S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[3]Stockwell R G.S-transform analysis of gravity waveactivity from a small scale network of airglow im-agers[D].Ontario London:the University of West-ern Ontario,1999.
[4]Mcfadden P D,Cook J G,Forster L M.Decomposi-tion of gear vibration signals by the generalized Stransform[J].Mechanical System and Signal Pro-cessing,1999,13(5):691-707.
[5]Livanos G,Ranganathan N,Jiang J.Heart soundanalysis using the S-transform[J].IEEE Computersin Cardiology,2000,27:587-590.
[6]Theophanis S,Queen J.Color display of the local-ized spectrum[J].Geophysics,2000,65(4):1330-1340.
[7]Pinnegar C R,Mansinha L.The S-transform withwindows of arbitrary and varying shape[J].Geo-physics,2003,68(1):381-385.
[8]高静怀,陈文超,李幼铭,等.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,46(4):526-532.
[9]Pinnegar C R,Eaton D W.Application of the Stransform to prestack noise attention filtering[J].Journal of Geophysical Research,2003,108(B9):2422-2431.
[10]陈学华.时频分布与地震信号谱分析研究[D].成都:成都理工大学信息工程学院,2006.
[2]Stockwell R G,Mansinha L,Lowe R P.Localiza-tion of the complex spectrum:the S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[3]Stockwell R G.S-transform analysis of gravity waveactivity from a small scale network of airglow im-agers[D].Ontario London:the University of West-ern Ontario,1999.
[4]Mcfadden P D,Cook J G,Forster L M.Decomposi-tion of gear vibration signals by the generalized Stransform[J].Mechanical System and Signal Pro-cessing,1999,13(5):691-707.
[5]Livanos G,Ranganathan N,Jiang J.Heart soundanalysis using the S-transform[J].IEEE Computersin Cardiology,2000,27:587-590.
[6]Theophanis S,Queen J.Color display of the local-ized spectrum[J].Geophysics,2000,65(4):1330-1340.
[7]Pinnegar C R,Mansinha L.The S-transform withwindows of arbitrary and varying shape[J].Geo-physics,2003,68(1):381-385.
[8]高静怀,陈文超,李幼铭,等.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,46(4):526-532.
[9]Pinnegar C R,Eaton D W.Application of the Stransform to prestack noise attention filtering[J].Journal of Geophysical Research,2003,108(B9):2422-2431.
[10]陈学华.时频分布与地震信号谱分析研究[D].成都:成都理工大学信息工程学院,2006.
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