Abstract:
The paper is devoted to the sufficient conditions for the asymptotical separation of distinct terms in the linear combination of harmonics by Singular Spectrum Analysis (briefly, SSA). Namely, let $x_0, ..., x_{N-1}$ be the series with $x_n = \sum_{i = 1}^{n} f_{i,n}$ where $f_{i,n} = b_i \cos(\omega_in + \gamma_i)$, and both amplitudes $|b_i|$ and frequencies $\omega_i \in (0, 1/2)$ are pairwise different. Then it s proved that under some relationship between amplitudes $|b_i|$ and the standard choice of SSA parameters the so-called reconstruction values $\tilde{f}_{i,n}$ become very close to $f_{i,n}$ for big $N$. Moreover, $\max_n(|\tilde{f}_{i,n} - f_{i,n}|) = O(N^{-1})$ for any $i$ as $N \to \infty$.
Keywords:signal processing, singular spectral analysis, linear combination of harmonics, separability of harmonics, asymptotical analysis.
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