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.
引用
收藏
页码：1164 / 1170
页数：7
相关论文
共 50 条
  • [31] Intrusion Detection System using Discrete Fourier Transform
    Chimedtseren, Enkhbold
    Iwai, Keisuke
    Tanaka, Hidema
    Kurokawa, Takakazu
    2014 SEVENTH IEEE SYMPOSIUM ON COMPUTATIONAL INTELLIGENCE FOR SECURITY AND DEFENSE APPLICATIONS (CISDA), 2014, : 41 - 45
  • [32] Channel estimation using discrete Fourier transform techniques
    Tellambura, C.
    Parker, Matthew G.
    Barton, S.K.
    Conference Record / IEEE Global Telecommunications Conference, 1998, 1 : 148 - 152
  • [33] Discrete Fourier Transform Computation Using Neural Networks
    Velik, Rosemarie
    2008 INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND SECURITY, VOLS 1 AND 2, PROCEEDINGS, 2008, : 120 - 123
  • [34] Frequency estimation using warped discrete Fourier transform
    Franz, S
    Mitra, SK
    Doblinger, G
    SIGNAL PROCESSING, 2003, 83 (08) : 1661 - 1671
  • [35] Image Steganography using Discrete Fractional Fourier Transform
    Soni, Ashish
    Jain, Jitendra
    Roshan, Rakesh
    2013 INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS AND SIGNAL PROCESSING (ISSP), 2013, : 97 - 100
  • [36] Capturing recurring concepts using discrete Fourier transform
    Sakthithasan, Sripirakas
    Pears, Russel
    CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE, 2016, 28 (15): : 4013 - 4035
  • [37] Channel estimation using discrete Fourier transform techniques
    Tellambura, C
    Parker, MG
    Barton, SK
    GLOBECOM 98: IEEE GLOBECOM 1998 - CONFERENCE RECORD, VOLS 1-6: THE BRIDGE TO GLOBAL INTEGRATION, 1998, : 148 - 152
  • [38] Image compression using discrete fractional Fourier transform
    Cong, WX
    Lin, ZK
    Zhu, HQ
    PROCEEDINGS OF FOURTH INTERNATIONAL WORKSHOP ON CSCW IN DESIGN, 1999, : 433 - 436
  • [39] Abnormal gait detection using discrete Fourier transform
    Mostayed, Ahmed
    Mazumder, Mohammad Mynuddin Gani
    Kim, Sikyung
    Park, Se Jin
    MUE: 2008 INTERNATIONAL CONFERENCE ON MULTIMEDIA AND UBIQUITOUS ENGINEERING, PROCEEDINGS, 2008, : 36 - +
  • [40] BEURLING'S THEOREM FOR THE Q-FOURIER-DUNKL TRANSFORM
    Loualid, El Mehdi
    Achak, Azzedine
    Daher, Radouan
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2021, 45 (01): : 39 - 46
12345