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Volume 32, Issue 4
A Remark on Adaptive Decomposition for Nonlinear Time-Frequency Analysis

Xu Liu & Haina Wang

DOI: 10.13447/j.1674-5647.2016.04.03

Commun. Math. Res., 32 (2016), pp. 319-324.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

Hilbert transform, empirical mode decomposition, adaptive decomposition algorithm, best approximation.

  • AMS Subject Headings

46E20, 46A35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-319, author = {Liu , Xu and Wang , Haina}, title = {A Remark on Adaptive Decomposition for Nonlinear Time-Frequency Analysis}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {4}, pages = {319--324}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.04.03}, url = {http://global-sci.org/intro/article_detail/cmr/18903.html} }
TY - JOUR T1 - A Remark on Adaptive Decomposition for Nonlinear Time-Frequency Analysis AU - Liu , Xu AU - Wang , Haina JO - Communications in Mathematical Research VL - 4 SP - 319 EP - 324 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.04.03 UR - https://global-sci.org/intro/article_detail/cmr/18903.html KW - Hilbert transform, empirical mode decomposition, adaptive decomposition algorithm, best approximation. AB -

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.

Liu , Xu and Wang , Haina. (2021). A Remark on Adaptive Decomposition for Nonlinear Time-Frequency Analysis. Communications in Mathematical Research . 32 (4). 319-324. doi:10.13447/j.1674-5647.2016.04.03
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