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首页> 外文期刊>IEEE Transactions on Automatic Control >Symbolic dynamics for processing chaotic signals-I: noise reduction of chaotic sequences
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Symbolic dynamics for processing chaotic signals-I: noise reduction of chaotic sequences

机译：混沌信号处理的符号动力学-I：混沌序列的降噪

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Chaotic signals attracted the attention among researchers because of their rich dynamics and their random-like behavior. What has been missing so far is an appropriate characterization of chaotic systems from a signal-processing point of view. This paper demonstrates that the framework of symbolic dynamics gives the possibility to partition the infinite number of finite-length trajectories of the piecewise-linear chaotic system into a countable number of trajectory-sets with common statistical properties. It turns out that this partitioning allows to derive noise-reduction schemes directly from the maximum-likelihood criteria. For the two proposed noise-reduction methods, the upper performance limits are given in an analytical form and the results are verified by applying the schemes to different types of one dimensional piecewise-linear Markov maps.
机译：混沌信号因其丰富的动态和随机行为而引起了研究人员的注意。到目前为止，缺少的是从信号处理的角度对混沌系统进行适当的表征。本文表明，符号动力学框架提供了将分段线性混沌系统的无限个有限长度轨迹划分为具有共同统计性质的可计数轨迹集的可能性。事实证明，这种分区允许直接从最大似然准则中推导出降噪方案。对于所提出的两种降噪方法，以解析形式给出了性能上限，并将该方案应用于不同类型的一维分段线性马尔可夫映射，对结果进行了验证。

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