Sparse Sampling in Fractional Fourier Domain: Recovery Guarantees and
Cramér-Rao Bounds
Cramér-Rao Bounds
File(s)
Preprint
Author(s)
Pavlíček, Václav
Bhandari, Ayush
Type
preprint
Abstract
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional concept of bandwidth and accommodating a wider range of functions that may not be bandlimited in the Fourier sense. Beyond bandlimited functions, sampling and recovery of sparse signals has also been studied in the FrFT domain. Existing methods for sparse recovery typically operate in the transform domain, capitalizing on the spectral features of spikes in the FrFT domain. Our paper contributes two new theoretical advancements in this area. First, we introduce a novel time-domain sparse recovery method that avoids the typical bottlenecks of transform domain methods, such as spectral leakage. This method is backed by a sparse sampling theorem applicable to arbitrary FrFT-bandlimited kernels and is validated through a hardware experiment. Second, we present Cramér-Rao Bounds for the sparse sampling problem, addressing a gap in existing literature.
Date Issued
2024-04-29
Citation
arXiv, 2024
Journal / Book Title
arXiv
Copyright Statement
Copyright © 2024 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
http://arxiv.org/abs/2404.18850v1
Subjects
cs.IT
cs.IT
eess.SP
math.IT