Adaptive iterative filtering methods for nonlinear signal analysis and applications

Time-frequency analysis;EMD;Iterative filtering;ALIF;Instantaneous frequency

Liu, Jingfang ; Zhou, Hao Min Mathematics Kang, Sung Ha Dieci, Luca Chow, Edmond Chow, Shui-Nee ; Zhou, Hao Min

University:Georgia Institute of Technology

Department:Mathematics

关键词: Time-frequency analysis;    EMD;    Iterative filtering;    ALIF;    Instantaneous frequency;   

Others  :  https://smartech.gatech.edu/bitstream/1853/52169/1/LIU-DISSERTATION-2013.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decompositionreally helps in both simulated data analysis and real world application.