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NAFASS: Discrete spectroscopy of random signals

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  • Nigmatullin, R.R.
  • Osokin, S.I.
  • Toboev, V.A.

Abstract

In this paper we suggest a new discrete spectroscopy for analysis of random signals and fluctuations. This discrete spectroscopy is based on successful solution of the modified Prony’s problem for the strongly-correlated random sequences. As opposed to the general Prony’s problem where the set of frequencies is supposed to be unknown in the new approach suggested the distribution of the unknown frequencies can be found for the strongly-correlated random sequences. Preliminary information about the frequency distribution facilitates the calculations and attaches an additional stability in the presence of a noise. This spectroscopy uses only the informative-significant frequency band that helps to fit the given signal with high accuracy. It means that any random signal measured in t-domain can be “read” in terms of its amplitude-frequency response (AFR) without model assumptions related to the behavior of this signal in the frequency region. The method overcomes some essential drawbacks of the conventional Prony’s method and can be determined as the non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS). In this paper we outline the basic principles of the NAFASS procedure and show its high potential possibilities based on analysis of some actual NIR data. The AFR obtained serves as a specific fingerprint and contains all necessary information which is sufficient for calibration and classification of the informative-significant band frequencies that the complex or nanoscopic system studied might have.

Suggested Citation

  • Nigmatullin, R.R. & Osokin, S.I. & Toboev, V.A., 2011. "NAFASS: Discrete spectroscopy of random signals," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 226-240.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:226-240
    DOI: 10.1016/j.chaos.2011.02.003
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    References listed on IDEAS

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    1. Al-Hasan, Mohammed & Nigmatullin, Raoul R., 2003. "Identification of the generalized Weibull distribution in wind speed data by the Eigen-coordinates method," Renewable Energy, Elsevier, vol. 28(1), pages 93-110.
    2. Kundu, Debasis, 1994. "Estimating the parameters of complex-valued exponential signals," Computational Statistics & Data Analysis, Elsevier, vol. 18(5), pages 525-534, December.
    3. Nigmatullin, R.R., 2000. "Recognition of nonextensive statistical distributions by the eigencoordinates method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(3), pages 547-565.
    4. Nigmatullin, R.R. & Smith, G., 2003. "Fluctuation-noise spectroscopy and a “universal” fitting function of amplitudes of random sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 291-317.
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