Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC

Bhandari, Ayush; Krahmer, Felix; Poskitt, Thomas

doi:10.48550/arxiv.2105.05818

Cited by 4 publications

(16 citation statements)

References 22 publications

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“…Moving on, there has recently been a great deal of activity in the signal processing community around recovery from modulo-reduced measurements [Bhandari et al, 2017, Ordentlich et al, 2018, Bhandari et al, 2018, Graf et al, 2019, Romanov and Ordentlich, 2019, Bhandari et al, 2020, Bhandari et al, 2021, Weiss et al, 2021. Most relevant to this paper is a line of works dealing with recovery from modulo-reduced measurements, and motivated by the modulo-ADC architecture described before Erez, 2017,Ordentlich et al, 2018].…”

Section: Related Workmentioning

confidence: 99%

Spiked Covariance Estimation from Modulo-Reduced Measurements

Romanov¹,

Ordentlich²

2021

Preprint

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Consider the rank-1 spiked model: X = √ u + Z, where is the spike intensity, u ∈ −1 is an unknown direction and ∼ (0, 1), Z ∼ (0, I). Motivated by recent advances in analog-to-digital conversion, we study the problem of recovering u ∈focusing on the high-dimensional regime ( 1). We develop and analyze an algorithm that, for most directions u and = poly( ), estimates u to high accuracy using = poly( ) measurements, provided that Δ log . Up to constants, our algorithm accurately estimates u at the smallest possible Δ that allows (in an information-theoretic sense) to recover X from Y. A key step in our analysis involves estimating the probability that a line segment of length ≈ √ in a random direction u passes near a point in the lattice Δℤ . Numerical experiments show that the developed algorithm performs well even in a non-asymptotic setting.

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Section: Related Workmentioning

confidence: 99%

Spiked Covariance Estimation from Modulo-Reduced Measurements

Romanov¹,

Ordentlich²

2021

Preprint

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“…Let's review some important propositions and conclusions in [16,26]. Proposition 1 (Modular decomposition roperty) [16] Let g ∈ B Ω (Space of Ω-bandlimited functions) and M λ (•) be defined in (7) where λ is a fixed, positive constant.…”

Section: Unlimited Sampling Theorem In Fourier Domainmentioning

confidence: 99%

“…[25] The unlimited sampling method based on wavelet is suitable for general smooth signals, not limited to bandlimited signals. [26] is mainly applicable to bandlimited signals in the Fourier domain (FD) on unlimited sampling method.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the above reasons, we put forward the problem on unlimited sampling of high dynamic non-bandlimited signals in the FD based on the FRFT. we innovate the content of [26], and propose a new FRFD reconstruction theory of high dynamic non-bandlimited signals in the FD based on unlimited sampling framework. First, the modular nonlinear folding is performed in the FRFD for modular arithmetic.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Reconstruction Algorithm based on Fractional Fourier Transform for Unlimited Sampling

Zhao

Li²

2021

Preprint

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The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. We study the unlimited sampling problem of high dynamic nonbandlimited signals in the Fourier domain (FD) based on the fractional Fourier transform (FRFT). First, the modular nonlinear folding is performed in the fractional Fourier domain (FRFD) for modular arithmetic. Then, the fractional spectrum is estimated for any folding time by means of annihilation filtering. Finally, a novel unlimited sampling algorithm in the FRFD is obtained. The results show that the non-bandlimited signal can be reconstructed in the FD based on the FRFT, and it is not affected by the ADC threshold.

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“…In the presence of noise, more than two channels are considered and a lattice-based optimization method is used for recovery. Modulo sampling has been extended to different problems and signal models such as periodic bandlimited signals [13], wavelets [14], mixture of sinusoids [15], finite-rate-of-innovation signals [16], multidimensional signals [17], sparse vector recovery [18,19], direction of arrival estimation [20], computed tomography [21], and graph signals [22].…”

Section: Introductionmentioning

confidence: 99%

Residual Recovery Algorithm For Modulo Sampling

Azar¹,

Mulleti²,

Eldar³

2021

Preprint

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Two important attributes of analog to digital converters (ADCs) are its sampling rate and dynamic range. The sampling rate should be greater than or equal to the Nyquist rate for bandlimited signals with bounded energy. It is also desired that the signals' dynamic range should be within that of the ADC's; otherwise, the signal will be clipped. A modulo operator has been recently suggested prior to sampling to restrict the dynamic range. Due to the nonlinearity of the modulo operation, the samples are distorted. Existing recovery algorithms to recover the signal from its modulo samples operate at a high sampling rate and are not robust in the presence of noise. In this paper, we propose a robust algorithm to recover the signal from the modulo samples which operates at lower sampling rate compared to existing techniques. We also show that our method has lower error compared to existing approaches for a given sampling rate, noise level, and dynamic range of the ADC. Our results lead to less constrained hardware design to address dynamic range issues while operating at the lowest rate possible.

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Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC

Cited by 4 publications

References 22 publications

Spiked Covariance Estimation from Modulo-Reduced Measurements

Spiked Covariance Estimation from Modulo-Reduced Measurements

A Novel Reconstruction Algorithm based on Fractional Fourier Transform for Unlimited Sampling

Residual Recovery Algorithm For Modulo Sampling

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