Kavli Affiliate: Zheng Zhu
| First 5 Authors: Qi Zhang, Jiang Zhu, Fengzhong Qu, Zheng Zhu, De Wen Soh
| Summary:
Unlimited sampling was recently introduced to deal with the clipping or
saturation of measurements where a modulo operator is applied before sampling.
In this paper, we investigate the identifiability of the model where
measurements are acquired under a discrete Fourier transform (DFT) sensing
matrix first followed by a modulo operator (modulo-DFT). Firstly, based on the
theorems of cyclotomic polynomials, we derive a sufficient condition for
uniquely identifying the original signal in modulo-DFT. Additionally, for
periodic bandlimited signals (PBSs) under unlimited sampling which can be
viewed as a special case of modulo-DFT, the necessary and sufficient condition
for the unique recovery of the original signal are provided. Moreover, we show
that when the oversampling factor exceeds $3(1+1/P)$, PBS is always
identifiable from the modulo samples, where $P$ is the number of harmonics
including the fundamental component in the positive frequency part.
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