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Frequency analysis of time series by polynomials orthogonal on the grid

  • Software and Information Technologies for Analysis and Estimation of Data, Represented as Images and Signals
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Abstract

The problem of finding periodic components in a given time series is examined. Our approach to the harmonic analysis is based on the integrated method resting on discrete transforms that employ orthogonal polynomials and trigonometric systems.

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References

  1. D. R. Brillindzher, Time Series: Data Analysis and Theory (Holden-day, San Francisco, 1975; Mir, Moscow, 1980).

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  2. I. I. Sharapudinov, Orthogonal Polynomials on Discrete Meshes (Izd-vo Dag. Gos. Ped. Un-ta, Makhachkala, 1997) [in Russian].

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  3. I. I. Sharapudinov, Mixed Series by Orthogonal Polynomials (DNTs RAN, Makhachkala, 2004) [in Russian].

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  4. T. Sharapudinov and T. Luguev, “Processing and Compression of Time Series by Orthogonal Polynomials,” in Proc. of the 8th International Conference “Pattern Recognition and Image Analysis: New Informational Technologies” (PRIA-8-2007) (Yoshkar-Ola, 2007), Vol. 2, pp. 44–47.

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Authors and Affiliations

  1. Dagestan Scientific Center, Russian Academy of Sciences, ul. Gadzhieva 45, Makhachkala, 367025, Russia

    T. I. Sharapudinov & T. S. Luguev

Authors
  1. T. I. Sharapudinov
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  2. T. S. Luguev
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Correspondence to T. I. Sharapudinov.

Additional information

Timur I. Sharapudinov was born in 1983. He graduated from the Faculty of Mathematics at Dagestan State University in 2005. At present he works at the Dagestan Scientific Center of the Russian Academy of Sciences as a junior researcher. His scientific interests include the theory of approximation of functions, analysis and processing of signals, and orthogonal polynomials. He is the author of seven papers.

Timur S. Luguev was born in 1983. He graduated from the Faculty of Mathematics at Dagestan State University in 2006. He is presently at the Dagestan Scientific Center of the Russian Academy of Sciences, Department of Mathematics and Informatics, as a researcher engineer. His scientific interests include analysis and processing of signals and the theory of approximation of functions. He is the author of ten papers.

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Sharapudinov, T.I., Luguev, T.S. Frequency analysis of time series by polynomials orthogonal on the grid. Pattern Recognit. Image Anal. 19, 562–564 (2009). https://doi.org/10.1134/S1054661809030249

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  • DOI: https://doi.org/10.1134/S1054661809030249

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