A Remark on Adaptive Decomposition for Nonlinear Time-frequency Analysis  

作　　者：LIU XU WANG HAI-NA Ma Fu-ming 

机构地区：[1]School of Applied Mathematics,Jilin University of Finance and Economics,Changchun,130117 [2]不详

出　　处：《Communications in Mathematical Research》2016年第4期319-324,共6页数学研究通讯（英文版）

基　　金：The NSF(11426113)of China;the Science and Technology Research Project(2014161,2014163)of Jilin Provincial Department of Education of China;the Project(20160520110JH)of Science and Technology Development Plan for Jilin Provincial

摘　　要：In recent study the bank of real square integrable functions that have nonlinear phases and admit a well-behaved Hilbert transform has been constructed for adaptive representation of nonlinear signals. We first show in this paper that the available basic functions are adequate for establishing an ideal adaptive decomposition algorithm. However, we also point out that the best approximation algorithm, which is a common strategy in decomposing a function into a sum of functions in a prescribed class of basis functions, should not be considered as a candidate for the ideal algorithm.In recent study the bank of real square integrable functions that have nonlinear phases and admit a well-behaved Hilbert transform has been constructed for adaptive representation of nonlinear signals. We first show in this paper that the available basic functions are adequate for establishing an ideal adaptive decomposition algorithm. However, we also point out that the best approximation algorithm, which is a common strategy in decomposing a function into a sum of functions in a prescribed class of basis functions, should not be considered as a candidate for the ideal algorithm.

关 键 词：Hilbert transform empirical mode decomposition adaptive decompo-sition algorithm best approximation 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]