The general theoretical approach to the asymptotic extraction of the signal series from the
additively perturbed signal with the help of singular spectrum analysis (SSA) was already outlined in
Nekrutkin (2010, Stat. Its Interface 3, 297–319). In this paper, the example of such an analysis applied
to the linear signal and the additive sinusoidal noise is considered. It is proven that, in this case, the
so-called reconstruction errors ri(N) of SSA uniformly tend to zero as the series length N tends to
infinity. More precisely, we demonstrate that maxi |ri(N)| = O(N−1) as N → ∞ if the “window
length” L equals (N + 1)/2. It is important to mention that a completely different result is valid for
the increasing exponential signal and the same noise. As is proven in Ivanova and Nekrutkin (2019,
Stat. Its Interface 12(1), 49–59), no finite number of last terms of the error series tends to any finite
or infinite values in this case.