Year: 2025
Type: preprint
Abstract: The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), 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 $L^2(\mathbb R)$ is proposed, and the theoretical results are demonstrated through illustrative examples.
Source: arXiv (Cornell University)
Authors: Sahu, Vikash K., Lone, Waseem Z., Verma, Amit K.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7090725084
Cites:
Cited by:
Related to: