非厄米奇异谱分析在指数反演问题中的应用
Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem
摘要：
我们提出了一种新的方法来解决指数检索问题。我们推导出一个稳定的技术，基于奇异值分解（SVD）的滞后协方差和crosscovariance矩阵组成的协方差系数计算的索引翻译副本的初始时间序列。对于这些矩阵的广义特征值问题的解决。将初始信号映射到广义特征向量的基上，从而分析了相位图。模式识别技术可以应用于区分与指数和噪声相关的相图。每个频率通过展开相应肖像的相位、检测潜在的缠绕事件和估计相位斜率来评估。效率的建议和现有的方法进行了比较的一组例子，包括白高斯和自回归模型噪声。
英文摘要：
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.
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