Approximation of signals by general matrix summability with effects of Gibbs Phenomenon

B. B. Jena; Lakshmi Narayan Mishra; S. K. Paikray; U. K. Misra

doi:10.5269/bspm.v38i6.39280

B. B. Jena Veer Surendra Sai University of Technology Burla Department of Mathematics
Lakshmi Narayan Mishra Vellore Institute of Technology (VIT) University School of Advanced Sciences Department of Mathematics http://orcid.org/0000-0001-7774-7290
S. K. Paikray Veer Surendra Sai University of Technology Burla Department of Mathematics
U. K. Misra National Institute of Science and Technology Pallur Hills Berhampur Department of Mathematics

DOI: https://doi.org/10.5269/bspm.v38i6.39280

Keywords: Trigonometric approximation, Signal functions, Gibbs Phenomenon, Lp-norm

Abstract

In the proposed paper the degree of approximation of signals (functions) belonging to $Lip(\alpha,p_{n})$ class has been obtained using general sub-matrix summability and a new theorem is established that generalizes the results of Mittal and Singh [10] (see [M. L. Mittal and Mradul Veer Singh, Approximation of signals (functions) by trigonometric polynomials in $L_{p}$-norm, \textit{Int. J. Math. Math. Sci.,} \textbf{2014} (2014), Article

ID 267383, 1-6 ]). Furthermore, as regards to the convergence of Fourier series of the signals, the effect of the Gibbs Phenomenon has been presented with a comparison among different means that are generated from sub-matrix summability mean together with the partial sum of Fourier series of the signals.

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