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

Résumé

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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Références

D. H. Armitage and I. J. Maddox, A new type of Cesaro mean, Anal. 9 (1989), 195-204.

P. Chandra, A note on degree of approximation by Norlund and Riesz operators, Mat. Vestnik 42 (1990), 9-10.

P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002), 13-26.

U. Deger, ˙I. Dagadur, and M. Ku¸cukaslan, Approximation by trigonometric polynomials to functions in Lp-norm, Proc. Jangjeon Math. Soc. 15 (2012), 203-213.

V. N. Mishra, K. Khatri and L. N. Mishra, Product summability transform of conjugate series of Fourier series, Int. J. Math. Math. Sci. 2012 (2012), Article ID 298923, 1-14.

V. N. Mishra, K. Khatri and L. N. Mishra, Product (N, pn)(C, 1) summability of a sequence of Fourier coefficients, Math. Sci. 6 (2012), Article ID 38, 1-5.

M. L. Mittal and B. E. Rhoades, On the degree of approximation of continuous functions by using linear operators on their Fourier series, Int. J. Math. Game Theory Algebra, 9 (1999), 259-267.

M. L. Mittal and B. E. Rhoades, Degree of approximation to functions in a normed space, J. Comput. Anal. Appl. 2 (2000), 1-10.

M. L. Mittal, B. E. Rhoades, V. N. Mishra and Uaday Singh: Using infinite matrices to approximate functions of class Lip (α, p) using trigonometric polynomials, J. Math. Anal. Appl. 326 (2007), 667-676.

M. L. Mittal and Mradul Veer Singh, Approximation of signals (functions) by trigonometric polynomials in Lp-norm, Int. J. Math. Math. Sci. 2014 (2014), Article ID 267383, 1-6.

R. N. Mohapatra and D. C. Russell: Some direct and inverse theorems in approximation of functions, J. Austral. Math. Soc. (Ser. A) 34 (1983), 143-154.

J. A. Osikiewicz, Equivalence results for Cesáro submethods, Anal. 20 (2000), 35-43.

J. G. Proakis, Digital Communications, McGraw-Hill, New York 1985.

E. Z. Psarakis, G. V. Moustakides, An L2–based method for the design of 1-D zero phase FIR digital filters, IEEE Trans. Circuits Syst. I. Fundam. Theor. Appl. 44 (1997), 591-601.

E. S. Quade: Trigonometric approximation in the mean, Duke Math. J. 3 (1937), 529-542.

A. Zygmund, Trigonometric Series, third ed., Cambridge University Press, Cambridge, 2002.