FM~2let变换分解算法的研究
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摘要
FM2let变换分解力图采用最少的线性或非线性调频基函数来分解信号。FM2let变换分解算法的基本原理是利用信号的瞬时频率求得FM2let原子的5个参数,然后基于自适应匹配投影塔形分解思想实现FM2let变换的分解。FM2let变换分解算法在信号分析处理方面具有运算量小、运算速度快等优良的性能。FM2let谱分辨率高、抗噪性能好、参数数据量少,并且利用伪时频分布可以去除交叉项干扰。理论和实验证明,FM2let变换分解算法能对不同的信号结构表现出很强的适应性,能够简洁地表征信号时变或时不变特性。
A new decomposition algorithm named decomposition algorithm of FM2let transform is developed to decompose a signal by using a simplest group of linear or nonlinear FM basis functions.Its basic principle is to find 5 parameters of FM2let atom through estimation of instantaneous frequency,and then achieve the decomposition algorithm of FM2let transform based on adaptive pyramidal matching projection algorithm.The decomposition algorithm of FM2let transform has many excellent performances such as high calculation rate and low calculation capacity.It also has excellent features of high spectral resolution,good anti-noise performance and high compressibility,and can make cross-term free by using pseudo time-frequency distribution.Theoretical and experimental results show that the decomposition algorithm of FM2let transform has strong adaptability to different signal structures and gives concise representation of time-variable or time-invariable characteristic of signal.
A new decomposition algorithm named decomposition algorithm of FM2let transform is developed to decompose a signal by using a simplest group of linear or nonlinear FM basis functions.Its basic principle is to find 5 parameters of FM2let atom through estimation of instantaneous frequency,and then achieve the decomposition algorithm of FM2let transform based on adaptive pyramidal matching projection algorithm.The decomposition algorithm of FM2let transform has many excellent performances such as high calculation rate and low calculation capacity.It also has excellent features of high spectral resolution,good anti-noise performance and high compressibility,and can make cross-term free by using pseudo time-frequency distribution.Theoretical and experimental results show that the decomposition algorithm of FM2let transform has strong adaptability to different signal structures and gives concise representation of time-variable or time-invariable characteristic of signal.
引文
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[2]ZOUHong xing,DAIQiong hai,WANGRen ming,LIYan da.ParametricTFRviaWindowedExponentialFrequency ModulatedAtoms[J].IEEESignalProcessingLetters,2001,8(5):140-142.
[3]ZOUHong xing,LUXu guang,DAIQiong hai,LIYan da.SubspacesofFMmletTransform[J].ScienceinChina(Series F),2002,45(2):152-160.
[4]范万春.地震信号检测与事件识别技术研究[D].西安:西安交通大学博士论文,2003:40-60.
[5]QIAN.S.CHEND.SignalRepresentationviaAdaptiveNormalizedGaussianFunctions[J].IEEETrans.Signal Processing,1994,36(1):1-11.
[6]MALLATS,ZHANGZ.MatchingPursuitswithTime Frequency Dictionaries[J].IEEETrans.SignalProcessing,1993,41(12):3397-3415.
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