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Deriving the Variance of the Discrete Fourier Transform Test Using Parseval's Theorem

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Atsushi Iwasaki

Statistics Theory · Submitted 27 Jun 2018

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

The authors' main claim Numerical experiments are then used to show that this derived variance is robust.

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arXiv ID1806.10357 (version 2)
Pith IDPEYNM2MC, Pith's permanent record of this paper and its review
CitationAtsushi Iwasaki. "Deriving the Variance of the Discrete Fourier Transform Test Using Parseval's Theorem." arXiv:1806.10357 (2018). https://pith.science/paper/PEYNM2MC
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,153 input tokens.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.75 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.02 · states quantitative result 0.13 · compares with prior results 0.50 · mentions code or data availability 0.03.

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arXiv listing abstract v2. Results and the main claim are underlined; .

The discrete Fourier transform test is a randomness test included in NIST SP800-22. However, the variance of the test statistic is smaller than expected and the theoretical value of the variance is not known. Hitherto, the mechanism explaining why the former variance is smaller than expected has been qualitatively explained based on Parseval's theorem. In this paper, we explore this quantitatively and derive the variance using Parseval's theorem under particular assumptions. Numerical experiments are then used to show that this derived variance is robust.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The discrete Fourier transform test is a randomness test included in NIST SP800-22. background 1.00 0.04 0.02 asserted 1.00
s1 However, the variance of the test statistic is smaller than expected and the theoretical value of the variance is not known. gap 0.96 0.20 0.05 asserted 1.00
s2 Hitherto, the mechanism explaining why the former variance is smaller than expected has been qualitatively explained based on Parseval's theorem. background 0.72 0.05 0.04 asserted 0.98
s3 In this paper, we explore this quantitatively and derive the variance using Parseval's theorem under particular assumptions. contribution 0.92 0.95 0.21 asserted 0.96
s4 Numerical experiments are then used to show that this derived variance is robust. result 0.72 0.94 0.22 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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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

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Original abstract

The discrete Fourier transform test is a randomness test included in NIST SP800-22. However, the variance of the test statistic is smaller than expected and the theoretical value of the variance is not known. Hitherto, the mechanism explaining why the former variance is smaller than expected has been qualitatively explained based on Parseval's theorem. In this paper, we explore this quantitatively and derive the variance using Parseval's theorem under particular assumptions. Numerical experiments are then used to show that this derived variance is robust.

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