论文标题
非热奇异频谱分析应用于指数检索问题
Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem
论文作者
论文摘要
我们提出了一种解决指数检索问题的新方法。我们基于滞后和交叉协方差矩阵的奇异值分解（SVD）得出稳定的技术，该矩阵由针对初始时间序列的索引翻译副本计算的协方差系数组成。对于这些矩阵，解决了广义特征值问题。初始信号映射到广义特征向量的基础上，因此分析了相位肖像。模式识别技术可以应用于区分与指数和噪声相关的相位肖像。每个频率都通过相应肖像的拆开阶段进行评估，检测潜在的包装事件和相位斜率的估计。在一组示例（包括白色高斯和自动回归模型噪声）上比较了所提出的方法和现有方法的效率。
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients computed for index translated copies of an initial time series. For these matrices a generalized eigenvalue problem is solved. The initial signal is mapped into the basis of the generalized eigenvectors and phase portraits are consequently analyzed. Pattern recognition techniques could be applied to distinguish phase portraits related to the exponentials and noise. Each frequency is evaluated by unwrapping phases of the corresponding portrait, detecting potential wrapping events and estimation of the phase slope. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise.
