Automatic Statistical Time-Frequency Analysis

描述(申请人提供)：非平稳时间序列(即时间 具有随时间变化的统计特性的系列)出现在许多领域 神经科学研究和临床实践。例如，光谱 脑电(EEG)的特性随大脑状态而变化，并且 这种变异通常具有重要的临床或科学意义。 现有的谱分析方法假定时间序列是一种实现 一个平稳的随机过程。这些方法可以推广到非平稳情形。 进程使用加窗傅里叶变换，但 窗户必须是主观选择的。我们建议开发改进的、自动化的 非平稳多变量时间序列分析的统计方法。我们 将评估这些方法在实际模拟数据中的应用以及 脑部疾病患者所需的真实多通道脑电数据。我们 将我们的自动化方法的结果与临床判断进行比较。 我们的具体目标是开发、评估、应用、实施和分发 以下是统计方法： (1)一元随机变量时变功率谱的估计 (2)时变谱密度矩阵的估计器， 多变量随机过程的相干性和相位谱； 时频主成分分析；(4)时频滤波；(5) 循环旋转，以减少由于我们的估计器的二元结构而产生的偏差； (6)时间和时间都光滑的单变量和多变量过程 频域。 我们首次提出的统计方法是基于光滑局部化的 复指数(SLEX)变换，它提供了丰富的选择 正交变换。SLEX转换的结构允许我们使用 计算高效的Coifman和Wickerhauser最优基算法 自动选择表示分段的特定转换 非平稳时间序列分为近似平稳区间的时间序列。 我们提出的第二个方法(目标6)采取了一条新的道路。不同于传统的 专注于周期图建模的方法，我们建议对 传递函数直接作为频率和时间上的光滑函数 使用平滑样条线并使用信号加噪声模型。通过对 直接传递函数，我们在时间和时间上实现了同步平滑 傅里叶变换范围内的频率。与骨膜摄影术不同， 传递函数保留了相位信息，因此 可以直接计算时变的交叉谱、相干性和相位 从传递函数。

DESCRIPTION (provided by applicant): Non-stationary time series (i.e., time series with statistical properties that vary over time) arise in many areas of neuroscience research and clinical practice. For example, the spectral properties of electroencephalograms (EEGs) vary with brain state, and frequently this variation is of central clinical or scientific importance. Existing methods of spectra analysis assume that a time series is a realization of a stationary random process. These methods can be extended to non-stationary processes using windowed Fourier transforms, but the number and size of the windows must be chosen subjectively. We propose to develop improved, automatic statistical methods for analysis of non-stationary multivariate time series. We will evaluate the methods in applications to realistic simulated data and to real multi-channel EEG data required from patients with brain disorders. We will compare results from our automatic methods with the clinical judgments. Our specific aims are to develop, evaluate, apply, implement, and distribute the following statistical methods: (1) an estimator of the time-varying power spectrum of a univariate random process; (2) estimators of the time-varying spectral density matrix, coherences, and phase spectra of a multivariate random process; (3) time-frequency principal component analysis; (4) time-frequency filters; (5) cycle-spinning to reduce bias due to the dyadic structure of our estimators; and (6) univariate and multivariate processes that are smooth in both time and frequency domains. Our first proposed statistical methods are based on the Smooth Localized complex Exponential (SLEX) transform, which provides a rich selection of orthogonal transforms. The structure of the SLEX transform allows us to use the computationally efficient Best Basis algorithm of Coifman and Wickerhauser to automatically select a particular transform, which represents a segmentation of a non-stationary time series into approximately stationary intervals. Our second proposed approach (Aim 6) takes a new path. Unlike the traditional approaches that focus on modeling the Periodiograms, we propose to model the transfer function directly as a smooth function in both frequency and time using smoothing splines and to use a signal-plus-noise model. By modeling the transfer function directly, we alloy simultaneous smoothing in time and frequency within the Fourier transformation. Unlike the periodiogram, the transfer function preserves the phase information, and therefore the time-varying cross-spectra, coherence, and phase can be directly calculated from the transfer functions.