On the Identifiability from Modulo Measurements under DFT Sensing Matrix

Author:

Qi Zhang, Jiang Zhu, Fengzhong Qu, Zheng Zhu, De Wen Soh

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT), Signal Processing (eess.SP)

journal:

date:

2023-12-30 00:00:00

Abstract

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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