几种时频分析方法的比较及应用
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摘要
地震信号属于非平稳信号,常规傅立叶变换方法不能刻画任一时刻的频率成分,无法对其进行全面的分析。时频分析方法将一维时域信号变换到二维的时频平面,全面反映地震信号的时频联合特征。本文介绍了短时傅立叶变换、连续小波变换、Wigner-Ville分布、Cohen类分布四种时频分析方法,通过理论合成信号试算,从时间分辨率、频率分辨率,以及对多频率成份信号适应能力等方面阐述了这四种方法的优缺点,进一步分析比较了这四种方法的特点及应用效果。
The seismic data usually is non-stationary signal,so the Fourier transform can not show the news of frequency at anytime and the seismic data can not be analyzed comprehensively.Time-frequency analysis methods transform 1D time domain signal into 2D time-frequency domain plane,and describe the joint time-frequency characteristics of the seismic data.This paper introduces four methods of time-frequency analysis,such as short time Fourier transform,continuous wavelet transform,Wigner-Ville distribution and Cohen class distribution.This paper explaios the merits and defects of the methods from the time resolution,frequency resolution and the adaptive ability of multi-frequency signals.Moreover,this paper explains the traits and the applications of some methods further by some academic synthetic signal test.
The seismic data usually is non-stationary signal,so the Fourier transform can not show the news of frequency at anytime and the seismic data can not be analyzed comprehensively.Time-frequency analysis methods transform 1D time domain signal into 2D time-frequency domain plane,and describe the joint time-frequency characteristics of the seismic data.This paper introduces four methods of time-frequency analysis,such as short time Fourier transform,continuous wavelet transform,Wigner-Ville distribution and Cohen class distribution.This paper explaios the merits and defects of the methods from the time resolution,frequency resolution and the adaptive ability of multi-frequency signals.Moreover,this paper explains the traits and the applications of some methods further by some academic synthetic signal test.
引文
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[15]Jeffrey C,William J.Shift covariant time-frequen-cy distributions of discrete signals[J].1999,47(1):133~146.
[16]Jeffrey C,William J.A function of time,frequency[J],lag and doppler,1999,47(3):789~799.
[17]Jeffrey C,and Patrick F.Virtues and vices of quar-tic time-frequency distributions[J].IEEE Trans-actions on Signal Processing,2000,48(9):2641~2650.
[18]付丽华,李宏伟,张猛.基于小波变换的复杂噪声背景中谐波恢复方法[J].工程地球物理学报,2005(1).
[2]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1998.
[3]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].北京:人民邮电出版社,2006.
[4]Gabor D.Theory of Communication[J].Journal ofthe IEEE.1946,93:429~497.
[5]卫俊平.时频分析技术及应用[D].西安:电子科技大学,2005.
[6]Rioul,O,and M Vetterli.Wavelet and signal pro-cessing[J].IEEE Signal Processing,1991,8(4):14~38.
[7]Avijit Chakraborty,David Okaya.Frequency-timedecomposition of seismic data using wavelet-basedmethods[J].Geophysics,1995,60(6):1906~1916.
[8]胡昌华,李国华,刘涛,等.基于MATLAB 6.x的系统分析与设计——小波分析(第二版)[M].西安:电子科技大学出版社,2000.
[9]徐长发,李国宽.实用小波方法(第二版)[M].武汉:华中科技大学出版社,2004.
[10]Satish Sinha,Partha S Routh,etc.Spectral decom-position of seismic data with continuous-wavelettransform[J].Geophysics,2005,70(6):19~25.
[11]Hongbing Li,Wenzhi Zhao,etc.Measures of scalebased on the wavelet scalogram with applications toseismic attenuation[J],Geophysics.2006,71(5):111~118.
[12]Jeffrey C,William J.On the existence of discreteWigner distributions[J].IEEE Signal ProcessingLetters,1999,6(12):304~306.
[13]赵淑红.时频分析方法及其在地震数据处理中的应用[D].长安大学,2006.
[14]Cohen L.Generalized phase-space distributionfunctions[J].Jour.Math.Phys,1966,7:781~787.
[15]Jeffrey C,William J.Shift covariant time-frequen-cy distributions of discrete signals[J].1999,47(1):133~146.
[16]Jeffrey C,William J.A function of time,frequency[J],lag and doppler,1999,47(3):789~799.
[17]Jeffrey C,and Patrick F.Virtues and vices of quar-tic time-frequency distributions[J].IEEE Trans-actions on Signal Processing,2000,48(9):2641~2650.
[18]付丽华,李宏伟,张猛.基于小波变换的复杂噪声背景中谐波恢复方法[J].工程地球物理学报,2005(1).
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