Gibbs–Wilbraham oscillation related to an Hermite interpolation problem on the unit circle

Berriochoa, E.; Cachafeiro, A.; Amor, J.M. García

doi:10.1016/j.cam.2018.06.005

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…The traditional wavelet hard thresholding function is easy to produce Gibbs oscillation [15], while the soft thresholding method is easy to produce "over smooth" distortion due to the constant difference of wavelet coefficients [16].…”

Section: Signal Acquisition Andmentioning

confidence: 99%

Research on Spectrum Feature Identification of Indoor Multimodal Communication Signal

Chen

Liu

Fan

2021

Advances in Mathematical Physics

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In order to solve the problem of large signal acquisition error caused by radio wave multipath effect in indoor environment, firstly, the signal source carried on the motion platform is collected for spectrum signal, and the signal processed by wavelet threshold denoising algorithms extracted and stored for spectrum feature extraction. Then, after data training and identification, the signal source is input into the system in random mode for identification. The experimental results show that the improved fuzzy clustering algorithm (FCA) is 12.7% higher than the spectrum envelope extraction method (SEEM) in the recognition rate of spectrum characteristics of different modes of signal source.

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Section: Signal Acquisition Andmentioning

confidence: 99%

Research on Spectrum Feature Identification of Indoor Multimodal Communication Signal

Chen

Liu

Fan

2021

Advances in Mathematical Physics

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“…In that work it is also assumed the additional condition that the sequence {(φ * n ) } is uniformly bounded on T, where {φ n } is the sequence of monic orthogonal polynomials related to the measure and {φ * n } is the sequence of the reciprocal polynomials, (see [9]). In that situation studied in [15], properties (4)-6) also hold. Now, in the present paper we start from a different point of view because we base it on properties satisfied by the nodal systems and we do not need to consider orthogonality nor para-orthogonality with respect to any measure.…”

Section: Propositionmentioning

confidence: 76%

“…Remark 1. The nodal systems considered in [15] satisfy condition (1). Indeed they are the para-orthogonal polynomials related to measures in the Baxter class, (see [16]).…”

Section: Propositionmentioning

confidence: 99%

Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity

et al. 2020

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The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or paraorthogonal polynomials, which is an interesting approach because in practical applications this connection may not exist. A detailed study of the properties satisfied by the nodal system and the corresponding nodal polynomial is presented. We obtain the relevant results of the convergence related to the process for continuous smooth functions as well as the rate of convergence. Analogous results for interpolation on the bounded interval are deduced and finally some numerical examples are presented.

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Gibbs–Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle

Berriochoa

Cachafeiro

Amor

2020

Journal of Computational and Applied Mathematics

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Gibbs–Wilbraham oscillation related to an Hermite interpolation problem on the unit circle

Cited by 3 publications

References 3 publications

Research on Spectrum Feature Identification of Indoor Multimodal Communication Signal

Research on Spectrum Feature Identification of Indoor Multimodal Communication Signal

Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity

Gibbs–Wilbraham phenomenon on Lagrange interpolation based on analytic weights on the unit circle

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