A Class of Function-Preserving Neural Network Operators with Applications to Modulated Signal Denoising

Abstract

In this paper, we introduce a class of function-preserving neural network operators designed to preserve a prescribed strictly positive function. We examine the approximation behaviour of the proposed operators on the space of continuous functions and show that they are positive, linear, well-defined, and bounded. Specifically, we demonstrate uniform convergence on compact intervals and get quantitative estimates of the approximation error in terms of the modulus of continuity. To support the theoretical analysis, we present several numerical experiments focusing on the preservation of exponential and logarithmic functions. These examples show how well the proposed operators perform and compare them with existing neural network operators. Also, an application to denoising modulated signals is provided, demonstrating the practical relevance of the proposed approach.

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BibTeX

@misc{saini2026class,
  title = {{A Class of Function-Preserving Neural Network Operators with Applications to Modulated Signal Denoising}},
  author = {Sachin Saini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05759},
  eprint = {2610.05759},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05759},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - A Class of Function-Preserving Neural Network Operators with Applications to Modulated Signal Denoising
AU  - Sachin Saini
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05759
UR  - https://arxiv.org/abs/2610.05759
AB  - In this paper, we introduce a class of function-preserving neural network operators designed to preserve a prescribed strictly positive function. We examine the approximation behaviour of the proposed operators on the space of continuous functions and show that they are positive, linear, well-defined, and bounded. Specifically, we demonstrate uniform convergence on compact intervals and get quantitative estimates of the approximation error in terms of the modulus of continuity. To support the theoretical analysis, we present several numerical experiments focusing on the preservation of exponential and logarithmic functions. These examples show how well the proposed operators perform and compare them with existing neural network operators. Also, an application to denoising modulated signals is provided, demonstrating the practical relevance of the proposed approach.
ER  -

Abstract

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