Dynamical Sampling in Shift-Invariant Spaces Associated with multi-dimensional Special Affine Fourier Transform
Functional Analysis
2024-09-16 v1
Abstract
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical sampling problem in shift-invariant spaces associated with the multi-dimensional SAFT. Specifically, we derive a sufficient and necessary condition under which a function in a shift-invariant space can be stably recovered from its dynamical sampling measurements associated with the multi-dimensional SAFT . We also present a straightforward example to elucidate our main result.
Cite
@article{arxiv.2409.08506,
title = {Dynamical Sampling in Shift-Invariant Spaces Associated with multi-dimensional Special Affine Fourier Transform},
author = {Meng Ning and Li-Ping Wu and Qing-yue Zhang and Bei Liu},
journal= {arXiv preprint arXiv:2409.08506},
year = {2024}
}
Comments
22 pages, 11 figures