The paper has examined various aspects of the singular spectrum analysis (SSA) method. The original purpose of the method is to optimize harmonic (spectral) analysis of time series. A theoretical justification based on integral equations was given for the SSA. A solution to the problem of large dimensionality of the autocovariance matrix (AM) was proposed. A method for estimating the periods of AM eigenvectors considered as basis time functions (BTF) was put forward. The problems of repetitive frequencies and frequency overlaps in the BTF structure were discussed. Those overlaps could have lower or higher frequences than the main BTF one. A possibility of distortion of the BTF period estimate due to relatively high-frequency superpositions was noted. To solve this problem, a modification of SSA (SSA-HC) has been proposed, that allows for a more correct and effective solution to the main problem. The solutions to problems were supported by numerical examples.