Abstract: General approach to asymptotic signal extraction from an additively perturbed series with the help of Singular Spectrum Analysis (SSA) has already been described in [5]. This paper considers an example of this analysis applied to a polynomial signal and additive noise as linear combination of harmonics. In this case, the so-called reconstruction errors ri(N) of SSA have been found to uniformly tend to zero as the series length N tends to infinity. More precisely, we have proved that maxi |ri(N)| = O(N–1) as N → ∞ and for a “window length” L ~ αN, α ∈ (0, 1). This solves the problem of the accuracy of asymptotic separation of a polynomial signal from the seasonal component. The results on discrete Chebyshev polynomials in equally spaced points are essentially used to go to a polynomial of an arbitrary order from a linear signal, which was addressed for the case L = (N + 1)/2 in [7].
Original languageEnglish
Pages (from-to)144-154
Number of pages11
JournalVestnik St. Petersburg University: Mathematics
Volume59
Issue number2
DOIs
StatePublished - 1 Jun 2026

    Research areas

  • asymptotic analysis, discrete Chebyshev polynomials, polynomial signal, separability, signal processing, singular spectrum analysis

ID: 153215681