Graben P
Universität Potsdam, P.O. Box 601553, Institute of Linguistics, D-14415 Potsdam, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 1):051104. doi: 10.1103/PhysRevE.64.051104. Epub 2001 Oct 16.
We investigate the effect of symbolic encoding applied to times series consisting of some deterministic signal and additive noise, as well as time series given by a deterministic signal with randomly distributed initial conditions as a model of event-related brain potentials. We introduce an estimator of the signal-to-noise ratio (SNR) of the system by means of time averages of running complexity measures such as Shannon and Rényi entropies, and prove its asymptotical equivalence with the linear SNR in the case of Shannon entropies of symbol distributions. A SNR improvement factor is defined, exhibiting a maximum for intermediate values of noise amplitude in analogy to stochastic resonance phenomena. We demonstrate that the maximum of the SNR improvement factor can be shifted toward smaller noise amplitudes by using higher order Rényi entropies instead of the Shannon entropy. For a further improvement of the SNR, a half wave encoding of noisy time series is introduced. Finally, we discuss the effect of noisy phases on the linear SNR as well as on the SNR defined by symbolic dynamics. It is shown that longer symbol sequences yield an improvement of the latter.
我们研究了符号编码应用于由确定性信号和加性噪声组成的时间序列以及由具有随机分布初始条件的确定性信号给出的时间序列（作为事件相关脑电位模型）的效果。我们通过运行复杂度度量（如香农熵和雷尼熵）的时间平均值引入系统信噪比（SNR）的估计器，并证明在符号分布的香农熵情况下它与线性SNR的渐近等价性。定义了一个SNR改善因子，类似于随机共振现象，它在噪声幅度的中间值处表现出最大值。我们证明，通过使用高阶雷尼熵而不是香农熵，SNR改善因子的最大值可以向较小的噪声幅度移动。为了进一步提高SNR，引入了有噪声时间序列的半波编码。最后，我们讨论了有噪声相位对线性SNR以及由符号动力学定义的SNR的影响。结果表明，较长的符号序列会提高后者。
