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

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), 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.

Keywords

• Trigonometric approximation
• Signal functions
• Gibbs Phenomenon
• Lp-norm