Special-Affine Wavelets: Multi-Resolution Analysis and Function Approximation in L^2(R)
Functional Analysis
2026-01-12 v1
Abstract
The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in , making it a powerful tool for advanced signal analysis. This work introduces a robust sampling theory and constructs multiresolution structures within the SAFT domain to support the formation of orthonormal bases. Motivated by the need for a sampling theorem applicable to band-limited signals in the SAFT framework, we establish a corresponding theoretical foundation. Furthermore, a method for constructing orthogonal bases in is proposed, and the theoretical results are demonstrated through illustrative examples.
Cite
@article{arxiv.2510.09612,
title = {Special-Affine Wavelets: Multi-Resolution Analysis and Function Approximation in L^2(R)},
author = {Vikash K. Sahu and Waseem Z. Lone and Amit K. Verma},
journal= {arXiv preprint arXiv:2510.09612},
year = {2026}
}