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Adaptive Weighted Variation Restricted Cesà ro Means on Walsh-Type Systems and Applications to Noise-Robust Signal Smoothing

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  • Anteneh Tilahun Adimasu

Abstract

We investigate the convergence and approximation properties of Cesà ro means of Walsh-type Fourier series for functions belonging to classes of weighted bounded variation. Working within the dyadic and 2-adic framework, we establish new sufficient conditions under which Cesà ro means exhibit improved stability and convergence behavior compared with ordinary partial sums. Our results extend and refine earlier theorems on summability by incorporating weighted variation constraints that capture fine structural features of functions with limited smoothness. As an application, we interpret Cesà ro-summed Walsh-type expansions as smoothing operators for dyadic signals and demonstrate their effectiveness in suppressing oscillations while preserving essential signal characteristics. These findings provide a rigorous theoretical foundation for the use of Cesà ro means in signal smoothing and related problems in dyadic harmonic analysis.

Suggested Citation

  • Anteneh Tilahun Adimasu, 2026. "Adaptive Weighted Variation Restricted Cesà ro Means on Walsh-Type Systems and Applications to Noise-Robust Signal Smoothing," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2026, pages 1-11, May.
    • Handle: RePEc:hin:jijmms:3110846
    DOI: 10.1155/ijmm/3110846
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