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Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem

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Document pages: 34 pages

Abstract: We present a new approach to solve the exponential retrieval problem. Wederive a stable technique, based on the singular value decomposition (SVD) oflag-covariance and crosscovariance matrices consisting of covariancecoefficients computed for index translated copies of an initial time series.For these matrices a generalized eigenvalue problem is solved. The initialsignal is mapped into the basis of the generalized eigenvectors and phaseportraits are consequently analyzed. Pattern recognition techniques could beapplied 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 ofexamples, including the white Gaussian and auto-regressive model noise.

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