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Multidimensional Iterative Filtering Method for the Decomposition of High-Dimensional Non-Stationary Signals

Multidimensional Iterative Filtering Method for the Decomposition of High-Dimensional Non-Stationary Signals
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Year:    2017

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 2 : pp. 278–298

Abstract

Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non-stationary and non-linear signals. Recently in [3] IF has been proved to be convergent for any $L^2$ signal and its stability has been also demonstrated through examples. Furthermore, in [3] the so called Fokker-Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time-frequency analysis of non-stationary high-dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high-dimensional FP filters, when applied to the decomposition of two dimensional signals.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2017.s05

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 2 : pp. 278–298

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:   

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