Unlimited sampling of bandpass signals: computational demodulation via undersampling
File(s)
Accepted version
Author(s)
Shtendel, Gal
Florescu, Dorian
Bhandari, Ayush
Type
Journal Article
Abstract
Bandpass signals are an important sub-class of bandlimited signals that naturally arise in a number of application areas but their high-frequency content poses an acquisition challenge. Consequently, “Bandpass Sampling Theory” has been investigated and applied in the literature. In this article, we consider the problem of modulo sampling of bandpass signals with the main goal of sampling and recovery of high dynamic range inputs. Our work is inspired by the Unlimited Sensing Framework (USF). In the USF, the modulo operation folds high dynamic range inputs into low dynamic range, modulo samples. This fundamentally avoids signal clipping. Given that the output of the modulo nonlinearity is non-bandlimited, bandpass sampling conditions never hold true. Yet, we show that bandpass signals can be recovered from a modulo representation despite the inevitable aliasing. Our main contribution includes proof of sampling theorems for recovery of bandpass signals from an undersampled representation, reaching sub-Nyquist sampling rates. On the recovery front, by considering both time- and frequency-domain perspectives, we provide a holistic view of the modulo bandpass sampling problem. On the hardware front, we include ideal, non-ideal and generalized modulo folding architectures that arise in the hardware implementation of modulo analog-to-digital converters. Numerical simulations corroborate our theoretical results. Bridging the theory–practice gap, we validate our results using hardware experiments, thus demonstrating the practical effectiveness of our methods.
Date Issued
2023-01-01
Date Acceptance
2023-08-25
Citation
IEEE Transactions on Signal Processing, 2023, 71, pp.4134-4145
ISSN
1053-587X
Publisher
Institute of Electrical and Electronics Engineers
Start Page
4134
End Page
4145
Journal / Book Title
IEEE Transactions on Signal Processing
Volume
71
Copyright Statement
Copyright © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects
ADC
ALGORITHM
Analog-to-digital conversion (ADC)
approximation
bandpass sampling
Baseband
Channel coding
Demodulation
DYNAMIC-RANGE
Engineering
Engineering, Electrical & Electronic
Hardware
modulo
MODULO
Radar imaging
Science & Technology
Sensors
Shannon sampling theory
Signal processing algorithms
Technology
Publication Status
Published
Date Publish Online
2023-09-22