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A Class of Intrinsic Trigonometric Mode Polynomials

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Approximation Theory XV: San Antonio 2016 (AT 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 201))

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Abstract

In this paper, we study a class of trigonometric polynomials that exhibit properties expected from intrinsic mode functions. In a series of lemmas, we provide sufficient conditions for a positiveness of the instantaneous frequency, number of zeros and extrema, and the proximity of upper and lower envelopes. The question of necessity of each of the conditions is discussed in numerical examples. We also introduce an orthonormal basis in \(L_2\) of weak intrinsic mode functions.

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Acknowledgements

The author is thankful for all the suggestions of the anonymous reviewers that greatly improved the exposition as well as for bringing to our attention the references [6, 7] about an effective matching pursuit process for EMD.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, One West University Blvd., Brownsville, TX, 78520, USA

    Vesselin Vatchev

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  1. Vesselin Vatchev
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Correspondence to Vesselin Vatchev .

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Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, USA

    Gregory E. Fasshauer

  2. Department of Mathematics, Vanderbilt University , Nashville, Tennessee, USA

    Larry L. Schumaker

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Vatchev, V. (2017). A Class of Intrinsic Trigonometric Mode Polynomials. In: Fasshauer, G., Schumaker, L. (eds) Approximation Theory XV: San Antonio 2016. AT 2016. Springer Proceedings in Mathematics & Statistics, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-319-59912-0_18

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