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arXiv · 2409.08506

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

Meng Ning·Li-Ping Wu·Qing-yue Zhang·Bei Liu
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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.

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Meng Ning, Li-Ping Wu, Qing-yue Zhang, Bei Liu. 2024-09-13. Dynamical Sampling in Shift-Invariant Spaces Associated with multi-dimensional Special Affine Fourier Transform. https://arxiv.org/abs/2409.08506

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