Theory of Local parameters in Time-Frequency Analysis and its Applications to Tracking States of Mental Stress

精神应激状态通常通过脑电图和/或心电图来测量和估计。由于这些信号的特征和心理状态随时间的变化而变化，我们必须将其作为非平稳数据处理。因此，我们必须发展有效的非平稳数据分析方法。时频分析理论是分析生物医学信号等非平稳信号的有力工具。在这个项目中，我们试图找到有效的参数，通过这些参数我们可以提取随机过程的本质特征，并分析和解释非平稳信号。在随机过程理论中，提出了多种有效带宽，并在许多分支中经常使用。然而，团结他们的努力却很少。我们提出了一类广义的无限有效带宽，它包含了所有必要的传统带宽。该类由Renyi的α阶熵定义，给出了带宽的统一表达式。我们称它们为阶带宽，w。w -的概念很容易扩展到非平稳分析。然后提出了基于时频分布的时变W-alpha算法，并通过仿真分析证明了时变W-alpha算法的有效性。我们将其应用于脑电分析，这些脑电分析来自于被内田-克雷佩林任务所施加精神压力的人。结果表明，该方法可以有效地跟踪脑电信号的带宽。气象条件是影响人类精神状态的重要因素。在这个项目的后期，我们开始开发分析气象数据的方法，即一些气象卫星的图像数据、温度数据、降雨数据等。我们尝试将信息理论概念，如熵和散度应用到我们的方法中。我们已经展示了这些信息理论概念对我们的目的是非常强大的。

The state of mental stress is often measured and estimated by using EEG and/or ECG. Since feature of these signals and the mental state change with time, we have to deal them as non-stationary data. Therefore we have to develop effective methods for non-stationary data analysis.The theory of time-frequency analysis is known as a powerful tool to analyze non-stationary signals like biomedical signals.In this project, we tried to find effective parameters by which we can extract essential characteristics of a random process and analyze and interpret the non-stationary signals. In the theory of random processes, many kind of effective bandwidths have been proposed and used very often in may branches. How ever there have been few effort to unity them. We proposed a general class of infinite effective bandwidths which includes all the essential traditional bandwidths. The class is defined by Renyi's alpha-order entropy and gives unified expression of the bandwidths. We call them alpha-order bandwidths, W-alpha. The concept of W-alpha is easily expand to non-stationary analysis. Then we proposed time varying W-alpha based of time-frequency distributions and showed that the time varying W-alpha is effective by simulation analysis. We applied them to EEG analysis measured from persons who are put mental stress by been a task of Uchida-Kraepelin. We showed the method is useful to track alpha-bandwidth of EEG.Meteorological conditions are essential factors which affect human mental state. In the late stage of this project, we began to develop methods to analyze meteorological data, that is, image data from some meteorological satellites, temperature data, rainfall data, etc. We tried apply information theoretical concepts, like entropy and divergence to our methods. We have been showing these information theoretical concepts are very powerful to our purpose.