Sparse sampling in fractional Fourier domain: recovery guarantees and Cramér-Rao Bounds
Author(s)
Pavlicek, Vaclav
Bhandari, Ayush
Type
Journal Article
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
2024-01-01
Date Acceptance
2024-05-01
Citation
IEEE Signal Processing Letters, 2024, 31, pp.1665-1669
ISSN
1070-9908
Publisher
Institute of Electrical and Electronics Engineers
Start Page
1665
End Page
1669
Journal / Book Title
IEEE Signal Processing Letters
Volume
31
Copyright Statement
Copyright © 2024 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Subjects
Annihilation
BAND-LIMITED SIGNALS
Cramer-Rao Bounds
Engineering
Engineering, Electrical & Electronic
EXPANSION
Fractional Fourier Transform
SERIES
Sparse Sampling
THEOREM
TRANSFORM
Publication Status
Published
Date Publish Online
2024-05-08