Dynamical Sampling in Shift-Invariant Spaces Associated with multi-dimensional Special Affine Fourier Transform

TL;DR

This paper investigates the conditions for stable recovery of functions in shift-invariant spaces from dynamical sampling measurements related to the multi-dimensional Special Affine Fourier Transform, extending signal processing tools.

Contribution

It provides a necessary and sufficient condition for stable dynamical sampling recovery in shift-invariant spaces associated with the multi-dimensional SAFT, a generalization of several transforms.

Findings

Derived a necessary and sufficient condition for stable recovery

Extended dynamical sampling theory to multi-dimensional SAFT

Provided an illustrative example of the main result

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.