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    <journal-meta>
      <journal-id journal-id-type="nlm-ta">Rea Press</journal-id>
      <journal-id journal-id-type="publisher-id">null</journal-id>
      <journal-title>Rea Press</journal-title><issn pub-type="ppub">3009-4496</issn><issn pub-type="epub">3009-4496</issn><publisher>
      	<publisher-name>Rea Press</publisher-name>
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    <article-meta>
      <article-id pub-id-type="doi">https://doi.org/10.22105/xb1jhb09</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Research Article</subject>
        </subj-group>
        <subj-group><subject>Bilinear Hilbert transform, Bedrosian identity, Nonlinear Fourier atoms.</subject></subj-group>
      </article-categories>
      <title-group>
        <article-title>Nonlinear Signal Decomposition with Bilinear Hilbert Transform: A Framework for Analytical Decision-Making Applications</article-title><subtitle>Nonlinear Signal Decomposition with Bilinear Hilbert Transform: A Framework for Analytical Decision-Making Applications</subtitle></title-group>
      <contrib-group><contrib contrib-type="author">
	<name name-style="western">
	<surname>Ma</surname>
		<given-names>Danna </given-names>
	</name>
	<aff>Department of Mathematics, South China Agricultural University, Guangzhou, China.</aff>
	</contrib></contrib-group>		
      <pub-date pub-type="ppub">
        <month>05</month>
        <year>2024</year>
      </pub-date>
      <pub-date pub-type="epub">
        <day>01</day>
        <month>05</month>
        <year>2024</year>
      </pub-date>
      <volume>1</volume>
      <issue>2</issue>
      <permissions>
        <copyright-statement>© 2024 Rea Press</copyright-statement>
        <copyright-year>2024</copyright-year>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/2.5/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</p></license>
      </permissions>
      <related-article related-article-type="companion" vol="2" page="e235" id="RA1" ext-link-type="pmc">
			<article-title>Nonlinear Signal Decomposition with Bilinear Hilbert Transform: A Framework for Analytical Decision-Making Applications</article-title>
      </related-article>
	  <abstract abstract-type="toc">
		<p>
			This note emphasizes a point of view on the Bilinear Hilbert Transform (BHT) in the Bedrosian identity, which is originally based on the conventional Hilbert Transform in the theory of analytic signals. We show that the generalized sinc functions from Möbius play a crucial role. We have demonstrated some properties of BHT: Riesz representation theorem, boundedness, and Bedrosian identity for BHT. The generalized sinc function is a special solution of the Bedrosian identity. After that, we consider some of the nonlinear sinc functions, which are also the solutions of the Bedrosian identity. Lastly, the nonlinear sinc function system is orthonormal. In addition, we propose a framework for analytical decision-making applications that leverages the properties of BHT. incorporating this framework into existing real-world systems further enhances the adaptability and responsiveness of decision-making models, positioning the BHT as a critical tool for optimizing processes in dynamic, data-rich environments.
		</p>
		</abstract>
    </article-meta>
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