Approximation of signals by general matrix summability with effects of Gibbs Phenomenon
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, Appr...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2019-05-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/39280 |
| _version_ | 1827767144459272192 |
|---|---|
| author | B. B. Jena Lakshmi Narayan Mishra S. K. Paikray U. K. Misra |
| author_facet | B. B. Jena Lakshmi Narayan Mishra S. K. Paikray U. K. Misra |
| author_sort | B. B. Jena |
| collection | DOAJ |
| description | 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), ArticleID 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.
|
| first_indexed | 2024-03-11T11:54:41Z |
| format | Article |
| id | doaj.art-431275b603e04c568f3466ba875a33a0 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:54:41Z |
| publishDate | 2019-05-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-431275b603e04c568f3466ba875a33a02023-11-08T20:07:12ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-05-0138610.5269/bspm.v38i6.39280Approximation of signals by general matrix summability with effects of Gibbs PhenomenonB. B. Jena0Lakshmi Narayan Mishra1S. K. Paikray2U. K. Misra3Veer Surendra Sai University of Technology Burla Department of MathematicsVellore Institute of Technology (VIT) University School of Advanced Sciences Department of MathematicsVeer Surendra Sai University of Technology Burla Department of MathematicsNational Institute of Science and Technology Pallur Hills Berhampur Department of MathematicsIn 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), ArticleID 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. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/39280Trigonometric approximationSignal functionsGibbs PhenomenonLp-norm |
| spellingShingle | B. B. Jena Lakshmi Narayan Mishra S. K. Paikray U. K. Misra Approximation of signals by general matrix summability with effects of Gibbs Phenomenon Boletim da Sociedade Paranaense de Matemática Trigonometric approximation Signal functions Gibbs Phenomenon Lp-norm |
| title | Approximation of signals by general matrix summability with effects of Gibbs Phenomenon |
| title_full | Approximation of signals by general matrix summability with effects of Gibbs Phenomenon |
| title_fullStr | Approximation of signals by general matrix summability with effects of Gibbs Phenomenon |
| title_full_unstemmed | Approximation of signals by general matrix summability with effects of Gibbs Phenomenon |
| title_short | Approximation of signals by general matrix summability with effects of Gibbs Phenomenon |
| title_sort | approximation of signals by general matrix summability with effects of gibbs phenomenon |
| topic | Trigonometric approximation Signal functions Gibbs Phenomenon Lp-norm |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/39280 |
| work_keys_str_mv | AT bbjena approximationofsignalsbygeneralmatrixsummabilitywitheffectsofgibbsphenomenon AT lakshminarayanmishra approximationofsignalsbygeneralmatrixsummabilitywitheffectsofgibbsphenomenon AT skpaikray approximationofsignalsbygeneralmatrixsummabilitywitheffectsofgibbsphenomenon AT ukmisra approximationofsignalsbygeneralmatrixsummabilitywitheffectsofgibbsphenomenon |