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

被引：17
作者：
Iwasaki, Atsushi [1 ]
机构：
[1] Kyoto Univ, Grad Sch Informat, Kyoto 6068501, Japan
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 02期
关键词：
Discrete Fourier transforms; Probability density function; Density functional theory; NIST; Generators; Gaussian distribution; Random number; statistical test; discrete Fourier transform;
D O I：
10.1109/TIT.2019.2947045
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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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页码：1164 / 1170
页数：7
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