IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v44y2011i4p226-240.html
   My bibliography  Save this article

NAFASS: Discrete spectroscopy of random signals

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077911000208
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2011.02.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Kundu, Debasis, 1994. "Estimating the parameters of complex-valued exponential signals," Computational Statistics & Data Analysis, Elsevier, vol. 18(5), pages 525-534, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Touré, Siaka, 2005. "Investigations on the Eigen‐coordinates method for the 2‐parameter weibull distribution of wind speed," Renewable Energy, Elsevier, vol. 30(4), pages 511-521.
    2. El Alimi, Souheil & Maatallah, Taher & Dahmouni, Anouar Wajdi & Ben Nasrallah, Sassi, 2012. "Modeling and investigation of the wind resource in the gulf of Tunis, Tunisia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(8), pages 5466-5478.
    3. Nigmatullin, Raoul R. & Toboev, Vyacheslav A. & Lino, Paolo & Maione, Guido, 2015. "Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 166-181.
    4. Gugliani, G.K. & Sarkar, A. & Ley, C. & Mandal, S., 2018. "New methods to assess wind resources in terms of wind speed, load, power and direction," Renewable Energy, Elsevier, vol. 129(PA), pages 168-182.
    5. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    6. 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.
    7. Feng, Runhuan & Jing, Xiaochen, 2017. "Analytical valuation and hedging of variable annuity guaranteed lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 36-48.
    8. Andréa Camila dos Santos Martins & Antonio Roberto Balbo & Dylan Jones & Leonardo Nepomuceno & Edilaine Martins Soler & Edméa Cássia Baptista, 2020. "A Hybrid Multi-Criteria Methodology for Solving the Sustainable Dispatch Problem," Sustainability, MDPI, vol. 12(17), pages 1-20, August.
    9. Navarro-Moreno, Jesús & Moreno-Kaiser, Javier & Fernández-Alcalá, Rosa María & Ruiz-Molina, Juan Carlos, 2013. "Widely linear prediction for transfer function models based on the infinite past," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 139-146.
    10. Nandi, Swagata & Kundu, Debasis & Srivastava, Rajesh Kumar, 2013. "Noise space decomposition method for two-dimensional sinusoidal model," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 147-161.
    11. Raoul Nigmatullin & Semyon Dorokhin & Alexander Ivchenko, 2021. "Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems," Mathematics, MDPI, vol. 9(4), pages 1-11, February.
    12. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:226-240. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.