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Indirect Time Series Analysis of Chaos and Its Applications to Designs of 1/f Noise Generators Using SC Circuits

Research Project

Project/Area Number 05836025
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 非線形科学
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

KOHDA Tohru  Kyushu Univ., Dept. of Comp. Sci. & Comm. Eng., Professor, 工学部, 教授 (20038102)

Co-Investigator(Kenkyū-buntansha) TSUNEDA Akio  Kyushu Univ., Dept. of Comp. Sci. & Comm. Eng., Research Associate, 工学部, 助手 (40274493)
OOHAMA Yasutada  Kyushu Univ., Dept. of Comp. Sci. & Comm. Eng., Associate Professor, 工学部, 助教授 (20243892)
MURAO Kenji  Miyazaki Univ., Dept. of Electrical & Electronic Eng., Professor, 工学部, 教授 (00040973)
NISHI Tetsuo  Kyushu Univ., Dept. of Comp. Sci. & Comm. Eng., Professor, 工学部, 教授 (40037908)
川根 祐二  九州大学, 工学部, 助手 (30214662)
古賀 利郎  九州大学, 工学部, 教授 (00037706)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1994: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1993: ¥800,000 (Direct Cost: ¥800,000)
KeywordsNonlinear Map / Chaos / Indirect Time Series Analysis / PF Operator / Invariant Density / Correlation Function / 1 / f雑音 / Galerkin近似 / 区間力学系 / スイッチトキャパシタ回路
Research Abstract

There are two kinds of time series analysis for one-dimensional discrete chaos. One of them is the "time-average technique" in which we evaluate certain statistics of a sample long-time trajectory with some initial value ; the other one is the "ensemble-average techinque" based on an absolutely continuous invariant measure of the map which is referred to as the "indirect method". Such an indirect method is expected to play an important role in theoretically understanding chaos. In fact, the Perron-Frobenius (PF) operator permits us to theoretically calculate the ensemble average of several statistics. However, this operator, denoted by P_r, cannot be calculated directly because of its infinite dimensionality. In this research, we have given an efficient algorithm for systematically calculating several statistics, which is based on the Galerkin approximation to the operator PP_r, on a suitable function space. Furthermore, we have presented switched capacitor (SC) circuits for generation of 1/f noise which simulate dynamical systems with Procaccia-Schuster-type maps.
Usually, statistics of a chaotic trajectory itself (i.e., real-valued sequence) have been investigated. Recently, however, we give simple methods to obtain binary sequences from chaotic trajectories. In spread spectrum systems and cryptosystems, binary sequences with good correlation properties are required. In this research, we have theoretically evaluated statistics of chaotic binary sequences by the ensemble-average technique based on the PF operator. It has been shown that such chaotic binary sequences have good correlation properties. Moreover, we have theoretically evaluated high-order statistics of chaotic real-valued and binary sequences. Thus we have showed that chaotic sequences generated by the Chebyshev maps have quite good statistical properties.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (69 results)

All Other

All Publications (69 results)

  • [Publications] 香田徹: "カオス2進系列の相関関数のPerron-Frobenius作用素に基づく厳密評価" 電子情報通信学会技術研究報告. CAS93-40. 97-100 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "One-Dimensional Chaos and Its Applications to PN Sequences for CDMA" Proceedings of JTC-CSCC'93. 1. 272-275 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Pseudonoise Sequences by Chaotic Nonlinear Maps and Their Correlation Properties" IEICE Trans. Communications. E-76B. 855-862 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Kohda: "Correlation Properties of PN Sequences for CDMA : Chaotic Binary Sequences, Gold Sequences, and Kasami Sequences" Proc. of URSI'93. 127-127 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "カオス2進系列の高次相関関数のPerron-Frobenius作用に基づく厳密評価" 第16回情報理論とその応用シンポジウム予稿集. 2. 379-382 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "カオスの間接的時系列解析法とその応用" システム制御情報学会誌. 37. 661-668 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Indirect Time Series Analysis of 1-D Chaos and Its Applications to Designs of Noise Generators and to Evaluations of Randomness of Pseudorandom Number Generator" Proc. The 7th TOYOTA Conference. 241-256 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "An Explicit Evaluation of Correlation Functions of Chebyshev Binary Sequences Based on Perron-Frobenius Operator" Proceedings of NOLTA'93. 3. 975-978 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 村尾健次: "ベキ乗回路を用いた離散力学系のSC回路実現とその応用" 電子情報通信学会技術研究報告. CAS93-95. 37-44 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Auto-/Cross-Correlation Functions of Chaotic Binary/Bit Sequences" Proc. of International Conference on Dynamical Systems and Chaos. 1. 331-334 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kenji Murao: "Switched Capacitor Circuit for 1/f Noise Generation Using A Power-Law Circuit" International Journal of Circuit Theory and Applications. 22. 221-232 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Correlation Properties of Chebyshev Binary/Bit Sequences" Proceedings of ISIT'94. 76-76 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Even-and Odd-Correlation Functions of Chaotic chebyshev Bit Sequences for CDMA" Proceedings of ISSSTA'94. 2. 391-395 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "A Study on Pseudonoise-Coded Image Communications" Proc. of SPIE's Visual Communications and Image Processing'94. 874-884 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kenji Murao: "Switched-Capacitor Circuit Realizations for Two-Dimensional Torus Map" Proceedings of NOLTA'94. 17-20 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "A Study on Statistics of Chaotic Sequences of Finite Period" Proceedings of NOLTA'94. 121-124 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "Explicit Evaluations of Correlation Functions of Chebyshev Binary and Bit Sequences Based on Perron-Frobenius Operator" IEICE Trans. Fundamentals. E77-A. 1794-1800 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "有限周期カオス2進系列の統計量の揺らぎ" 第17回情報理論とその応用シンポジウム予稿集. 1. 165-168 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 大濱 靖匡: "一次元写像から生成される擬似乱数の統計的性質" 第17回情報理論とその応用シンポジウム予稿集. 1. 193-196 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "可変長PN符号で周波数拡散した画像伝送" 第17回情報理論とその応用シンポジウム予稿集. 1. 405-408 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "擬似乱数とカオス" 応用統計学会17回シンポジウム講演予稿集. 26-31 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Anthony J. Lawrance: "On Higher-Order Correlations of Chaotic Sequences" 電子情報通信学会技術研究報告. NLP95-55. 31-34 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "離散力学系のカオスの確率論・統計論的解析" 電子情報通信学会技術研究報告. IT95-35. 7-13 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "カオスピット系列による非同期CDMA/DSシステムのピット誤り確率の評価" 第18回情報理論とその応用シンポジウム予稿集. 2. 593-596 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "可変長の拡散符号を用いたCDMAチャネルによる画像伝送について" 第18回情報理論とその応用シンポジウム予稿集. 2. 773-776 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Tohru Kohda: "On Distributions of Statistics of Chaotic Sequences" Proceedings of NOLTA'95. 2. 873-876 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "An Explicit Explicit Evaluation of Correlation Functions of Chaotic Binary Sequences based no Perron-Frobenius Operator" Technical Report of IEICE. CAS93-40. 97-100 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "One-Dimensional Chaos and Its Applications to PN Sequences for CDMA" Proc. of JTC-CSCC'93. 272-275 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Pseudonoise Sequences by Chaotic Nonlinear Maps and Their Correlation Properties" IEICE Trans., Communications. vol.E76-B,no.8. 855-862 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Correlation Properties of PN Sequences for CDMA : Chaotic Binary Sequences, Gold Sequences, and Kasami Sequences" Proc. of XXIVth General Assembly of the International Union of Radio Science. 127 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "An Explicit Evaluation of Higher-Order Correlation Functions of Chaotic Binary Sequences based on Perron-Frobenius Operator" Proc. of SITA '93. 379-382 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Indirect Time Series Analysis of Chaos and Its Applications" Journal of ISCIE. vol.37, no.11. 661-668 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Indirect Time Series Analysis of 1-D Chaos and Its Applications to Designs of Noise Generators and to Evaluations of Randomness of Pseudorandom Number Generator" Proc. The 7th TOYOTA Conference : Towards The Harnessing of Chaos. 241-256 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "An Explicit Evaluation of Correlation Functions of Chebyshev Binary Sequences Based on Perron-Frobenius Operator" Proc. of NOLTA '93. 975-978 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Murao: "Switched Capacitor Circuits for Discrete Dynamical Systems Using Power-Law Circuits" Technical Report of IEICE. CAS93-95. 37-44 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Auto-/Cross- Correlation Functions of Chaotic Binary/Bit Sequences" Proc. of International Conference on Dynamical Systems and Chaos. Vol.1. 331-334 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Murao: "Switched Capacitor Circuit for 1/f Noise Generation Using A Power-Law Circuit" International Journal of Circuit Theory and Applications. Vol.22. 221-232 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Correlation Properties of Chebyshev Binary/Bit Sequences" Proc. of 1994 IEEE International Symposium on Information Theory. 76 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Even-and Odd-Correlation Functions of Chaotic Chebyshev Bit Sequences for CDMA" Proc. of the IEEE Third International Symposium on Spread Spectrum Techniques and Applications. 391-395 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "A Study on Pseudonoise-Coded Image Communications" Proc. of SPIE's Visual Communications and Image Processing '94. 874-884 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Murao: "Switched-Capacitor Circuit Realizations for Two-Dimensional Torus Maps" Proc. of NOLTA '94. 17-20 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "A Study on Statistics of Chaotic Sequences of Finite Period" Proc. of NOLTA '94. 121-124 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Explicit Evaluations of Correlation Functions of Chebyshev Binary and Bit Sequences Based on Perron-Frobenius Operator" IEICE Transactions on Fundamentals. vol.E77-A,no.11. 1794-1800 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Fluctuations of Statistics of Chaotic Sequences of Finite Period" Proc. of SITA '94. 165-168 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Oohama: "Statistical Properties of Pseudo-Random Numbers Generated by One-Dimensional Maps" Proc. of SITA '94. 193-196 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Variable-Length-PN-Coded Image Communications through CDMA Channels" Proc. of SITA '94. 405-408 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Pseudo-Random Numbers and Chaos" Proc. of 17th Symposium of Applied Statistical Society of Japan. 26-31 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A.J.Lawrance: "On Higher-Order Correlations of Chaotic Sequences" Technical Report of IEICE. NLP95-55. 31-34 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Probabilistic and Statistical Analyzes for One-Dimensional Chaos" Technical Report f IEICE. IT95-35. 7-13 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "Evaluations of Bit Error Probabilities in Asynchronous CDMA/DS Systems Using Chaotic Bit Sequences" Proc. of SITA '95. 593-596 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "On Image Transmission through CDMA Channels Using Spreading Sequences of Variable-Length" Proc. of SITA '95. 773-776 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Kohda: "On Distributions of Statistics of Chaotic Sequences" Proc. of NOLTA '95. 873-876 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 香田徹: "擬似乱数とカオス" 応用統計学会第17回シンポジウム講演予稿集. 26-31 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Anthony J. Lawrance: "On Higher-Order Correlations of Chaotic Sequences" 電子情報通信学会技術研究報告. ILP95-55. 31-34 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 香田徹: "離散力学系のカオスの確率論・統計論的解析" 電子情報通信学会技術研究報告. NLP95-35. 7-13 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 香田徹: "カオスビット系列による非同期CDMA/DSシステムのビット誤り確率の評価" 第18回情報理論とその応用シンポジウム予稿集. 2. 593-596 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Tohru Kohda: "On Distributions of Statistics of Chaotic Sequences" Proceeding of NOLTA'95. 2. 873-876 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kenji Murao: "Switched Capacitor Circuit for 1/f Noise Generation Using A Power‐Law Circuit" Int.Jour.Circuit Theory and Applications. 22. 221-232 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tohru Kohda: "Correlation Properties of Chebyshev Binary/Bit Sequences" Proc.1994 IEEE Int.Sympo.on Information Theory. 76-76 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 村尾健次: "スイッチトキャパシタ回路による二次元トーラス写像の実現" 平成6年度電気関係学会九州支部連合大会講演論文集. 3-3 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tohru Kohda: "A Study on Statistics of Chaotic Sequences of Finite Period" Proceedings of NOLTA'94. 121-124 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Kenji Murao: "Switched‐Capacitor Circuit Realizations for Two‐Dimensional Torus Maps" Proceedings of NOLTA'94. 17-20 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tohru Kohda: "Explicit Evaluations of Correlation Functions of Chebyshev Binary and Bit Sequences Based on Perron‐Frobenius Operator" IEICE Trans,Fundamentals. E77‐A,11. 1794-1800 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Kohda: "One-Dimensional Chaos and Its Applications to PN Sequences for CDMA" Proc.JTC-CSCC'93. 1. 272-275 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kohda: "Pseudonoise Sequences by Chaotic Nonlinear Maps and Their Correlation Properties" IEICE Trans.E76-B. 855-862 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kohda: "Correlation Properties of PN Sequences for CDMA:Chaotic Binary Sequences,Gold Sequences,and Kasami Sequences" Proc.The 24th General Assembly of the International Union of Radio Science. 127-127 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 香田 徹: "1次元カオスの間接的時系列解析法" 日本機械学会71期全国大会講演論文集. E2434-E2434 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kohda: "〓Indirect〓 Time Series Analysis for 1-D Chaos with Applications to Evaluations of Statistical Properties of PRNG" Proc.1993 International Symposium on Nonlinear Theory and its Applications. 1. 269-274 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kohda: "An Explicit Evaluation of Correlation Functions of Chebyshev Binary Sequences Based on Perron-Frobenius Operator" Proc.1993 International Symposium on Nonlinear Theory and its Applications. 3. 975-978 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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