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Frequency Estimation of Multiple Sinusoids with Sub-Nyquist Sampling Sequences

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Shan Huang, Hong Sun, Haijian Zhang, Lei Yu

Information Theory · Submitted 3 Jan 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Numerical results show that this method is feasible and accurate at quite low sampling rates.

how it is stated · asserted 1.00 read the record →

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arXiv ID1601.00270 (version 1)
Pith ID3ND6QLXU, Pith's permanent record of this paper and its review
CitationHaijian Zhang, Hong Sun, Lei Yu, Shan Huang. "Frequency Estimation of Multiple Sinusoids with Sub-Nyquist Sampling Sequences." arXiv:1601.00270 (2016). https://pith.science/paper/3ND6QLXU
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,802 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.74 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.66 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using under-sampled samples. We analyze the impact of under-sampling and demonstrate that three sub-Nyquist sequences are general enough to estimate the frequencies under some condition. The frequencies estimated from one sequence are unfolded in frequency domain, and then the other two sequences are used to pick the correct frequencies from all possible frequencies. Simulations illustrate the validity of the theory. Numerical results show that this method is feasible and accurate at quite low sampling rates.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. background 1.00 0.05 0.03 asserted 0.68
s1 In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using under-sampled samples. contribution 0.96 0.92 0.20 asserted 0.99
s2 We analyze the impact of under-sampling and demonstrate that three sub-Nyquist sequences are general enough to estimate the frequencies under some condition. contribution 0.49 0.93 0.35 asserted 1.00
s3 The frequencies estimated from one sequence are unfolded in frequency domain, and then the other two sequences are used to pick the correct frequencies from all possible frequencies. method 1.00 0.78 0.13 asserted 0.99
s4 Simulations illustrate the validity of the theory. result 0.78 0.90 0.09 asserted 1.00
s5 Numerical results show that this method is feasible and accurate at quite low sampling rates. result 0.91 0.94 0.46 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.98.

What was examined, and what was not

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not examined
  • full text
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  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using under-sampled samples. We analyze the impact of under-sampling and demonstrate that three sub-Nyquist sequences are general enough to estimate the frequencies under some condition. The frequencies estimated from one sequence are unfolded in frequency domain, and then the other two sequences are used to pick the correct frequencies from all possible frequencies. Simulations illustrate the validity of the theory. Numerical results show that this method is feasible and accurate at quite low sampling rates.

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