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

混沌的间接时间序列分析及其在 SC 电路 1/f 噪声发生器设计中的应用

基本信息

批准号：
05836025
负责人：
KOHDA Tohru
金额：
$ 1.54万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05836025/
关键词：
Nonlinear 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

项目摘要

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.

一维离散混沌的时间序列分析方法有两种。其中一种是“时间平均技术”，它用一定的初值来估计样本长时间轨迹的某些统计量；另一种是基于映射的绝对连续不变度量的“集合平均技术”，称为“间接法”。这种间接的方法有望在从理论上理解混沌方面发挥重要作用。事实上，Perron-Frobenius(PF)算符允许我们在理论上计算几个统计量的集合平均。然而，由于它的无穷维性，这个算子P_r不能直接计算。在这项研究中，我们给出了一个在适当的函数空间上系统地计算几个统计量的有效算法，该算法基于对算子PP_r的Galerkin逼近。此外，我们还提出了用于产生1/f噪声的开关电容(SC)电路，用于模拟具有Procaccia-Schuster类型映射的动态系统。通常，我们还研究了混沌轨迹本身(即实值序列)的统计特性。然而，最近，我们给出了从混沌轨迹中获得二进制序列的简单方法。在扩频系统和密码系统中，需要具有良好的相关特性的二进制序列。在本研究中，我们利用基于PF算子的集成平均技术，从理论上评估了混沌二进制序列的统计特性。研究表明，这种混沌二进制序列具有良好的相关特性。此外，我们还从理论上评估了混沌实值序列和二值序列的高阶统计量。从而证明了由切比雪夫映射产生的混沌序列具有很好的统计特性。