Skip to main content
SpringerLink
Log in

The General Theory of Reproducible and Quasi-Reproducible Experiments

  • Chapter
  • First Online:
New Digital Signal Processing Methods

  • 470 Accesses

Abstract

This chapter represents the logical continuation of Chap. 5. Assuming that any set of reproducible/repeatable measurements can be considered as a quasi-periodic process, it is possible to derive the fitting function that strives to describe every experiment in which measurements of the same variable or quantity can be repeated many times. Here, it is essential to note that the conventional Fourier transform (F-transform) corresponds to an “ideal” experiment, in which all measurements taken during a long time are identical to each other. This chapter, instead, is focused on and gives answers for the case of non-stationary measurements, showing that any set of measurements contains two fitting functions: (a) the first one associated with the simple model with the minimal number of fitting parameters and (b) the second one following from the quasi-periodic process generated by repeated measurements. As in the rest of the book, this chapter contains some convincing arguments based on the analysis of real, available data. Nontrivial examples show how to apply the newly introduced idea on data that a reader may use in a laboratory. The final section contains an analysis of the results and further perspectives. A reading of this chapter even independently of the covered topics and examples could be useful and instructive.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Inc., Englewood Cliffs, 1975)

    Google Scholar 

  2. J. Singleton, A. Royce, B.C. Straits, M.M. Straits, Approaches to Social Research (Oxford University Press, Oxford, 1993)

    Google Scholar 

  3. J.M. Mendel, Lessons in Estimation Theory for Signal Processing, Communications, and Control (Pearson Education, London, 1995)

    Google Scholar 

  4. M.T. Hagan, H.B. Demuth, M.H. Beale, Neural network design (Pws Pub, Boston, 1996)

    Google Scholar 

  5. E.C. Ifeachor, B.W. Jervis, Digital Signal Processing: A Practical Approach (Pearson Education, London, 2002)

    Google Scholar 

  6. D.C. Montgomery, C.L. Jennings, M. Kulahci, Introduction to Time Series Analysis and Forecasting (Wiley, Hoboken, 2011)

    Google Scholar 

  7. J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, Hoboken, 2011)

    Google Scholar 

  8. A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, D.B. Rubin, Bayesian Data Analysis (CRC Press, Boca Raton, 2013)

    Book  Google Scholar 

  9. G.E.P. Box, G.M. Jenkins, G.C. Reinsel, Time Series Analysis: Forecasting and Control (Wiley, Oxford, 2013)

    Google Scholar 

  10. C. Chatfield, The Analysis of Time Series: An Introduction (CRC Press, Boca Raton, 2013)

    Google Scholar 

  11. R.R. Nigmatullin, Phys. Wave Phenom 16, 119 (2008)

    Article  Google Scholar 

  12. R.R. Nigmatullin, A.A. Khamzin, J.T. Machado, Phys. Scr. 89(1), 015201 (2014)

    Article  Google Scholar 

  13. R.R. Nigmatullin, R.M. Rakhmatullin, Commun. Nonlinear Sci. Numer. Simul 19, 4080 (2014)

    Article  Google Scholar 

  14. M.R. Osborne, G.K. Smyth, SIAM J. Sci. Stat. Comput 12, 362 (1991)

    Article  Google Scholar 

  15. M. Kahn, M.S. Mackisack, M.R. Osborne, G.K. Smyth, J. Comput. Graph. Stat. 1, 329 (1992)

    Google Scholar 

  16. M.R. Osborne, G.K. Smyth, SIAM J. Sci. Stat. Comput 16, 119 (1995)

    Article  Google Scholar 

  17. R.R. Nigmatullin, J. Appl. Nonlinear Dynam 1(2), 173–194 (2012)

    Article  Google Scholar 

  18. R.R. Nigmatullin, J. Appl. Nonlinear Dynam 1(3), 207–225 (2012)

    Article  MathSciNet  Google Scholar 

  19. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press. See Section 6.1, 1991)

    Google Scholar 

  20. S.M. Pershin, A.F. Bunkin, V.A. Lukyanchenko, R.R. Nigmatullin, Lazer Phys. Lett. 4, 809 (2007)

    Article  Google Scholar 

  21. R.R. Nigmatullin, R.M. Rakhmatullin, S.I. Osokin, Magn. Reson. Solids, (Electronic Journal) 16(2), 1 (2014). (http://mrsej.kpfu.ru)

    Google Scholar 

  22. R.R. Nigmatullin, W. Zhang, D. Striccoli, General theory of experiment containing reproducible data: The reduction to an ideal experiment. Commun. Nonlinear Sci. Numer. Simul. 27, 175–192 (2015)

    Article  MathSciNet  Google Scholar 

  23. R.R. Nigmatullin, S.I. Osokin, D. Baleanu, S. Al-Amri, A. Azam, A. Memic, The first observation of memory effects in the InfraRed (FT-IR) measurements: Do successive measurements remember each other? PLoS One, Open access journal 9(4), e94305 (2014)

    Article  Google Scholar 

  24. M. Kuczma, A servey of the theory of functional equations, Publikacije Elektrotehnickogo Fakulteta Univerziteta U Beogradu (Publications de La Faculted'electrotechniquede L'universitea Belgrade), 130 (1964), pp. 1–64

    Google Scholar 

  25. R.R. Nigmatullin, G. Maione, P. Lino, F. Saponaro, W. Zhang, The general theory of the quasi-reproducible experiments: How to describe the measured data of complex systems? Commun. Nonlinear Sci. Numer. Simul. 42, 324–341 (2017). https://doi.org/10.1016/j.cnsns.2016.05.019

    Article  Google Scholar 

  26. А. Wald, Successive Analysis (FizMatLit, Мoscow, 1960). (in Russian)

    MATH  Google Scholar 

  27. V.А. Kotelnikov, The Theory of Potential Noise Stability (Moscow-Leningrad GEI, 1956). (in Russian)

    Google Scholar 

  28. P.L. Stratonovich, Y.G. Sosulin, Optimal signal receiving on the background of the nongaussain disturbance. Radiotech. Electron (1966). (in Russian)

    Google Scholar 

  29. V.I. Tikhonov, Optimal Signals Reception (Radio and Contacts, Мoscow, 1983). (in Russian)

    Google Scholar 

  30. Y.D. Shirman, Resolution and Compression of Signals (Soviet Radio, Мoscow, 1974). (in Russian)

    Google Scholar 

  31. A.P. Triphonov, Y.S. Shinakov, Simultaneous Detection of Signals and Evaluation of their Parameters on the Disturbance Background (Radio and Contacts, Мoscow, 1986). (in Russian)

    Google Scholar 

  32. A.P. Triphonov, Reception of a signal with unknown duration on the “white” noise background. Radiotech. Electron 22(1), С. 435–С. 438 (1977). (in Russain)

    Google Scholar 

  33. А.I. Perov, Statistical Theory of Radiotechnical Systems (Radiotechnics, Мoscow, 2003). (in Russian)

    Google Scholar 

  34. V.I. Strokov, V.А. Pakhotin, V.М. Aniskevich, The application of the optimal reception theory for solution of the spatial signals resolution. Vestnik BFU 4, С. 69–73. (in Russian) (2014)

    Google Scholar 

  35. V.А. Pakhotin, А.I. Babinovich, V.I. Strokov, The maximal likelihood method in application to the low frequency-modulated signals. Vestnik BFU 4, С. 67–С. 74 (2015). (in Russian)

    Google Scholar 

  36. V.I. Strokov, V.А. Pakhotin, V.А. Bessonov, The peculiarities of receiving of superresolved signals with the help of the maximal likelihood theory. In the proceedings of the XXI International science-technical conference “Radiolocation, navigation and contacts” vol. 1, С. 230–241, 2015

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Radioelectronics and Informative-Measurement Technics Department, Kazan National Research Technical University named by A.N. Tupolev (KNRTU-KAI), Kazan, Tatarstan Republic, Russia

    Raoul R. Nigmatullin

  2. Department of Electrical and Information Engineering, Polytechnic University of Bari, Bari, Italy

    Paolo Lino & Guido Maione

Authors
  1. Raoul R. Nigmatullin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Lino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guido Maione
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nigmatullin, R.R., Lino, P., Maione, G. (2020). The General Theory of Reproducible and Quasi-Reproducible Experiments. In: New Digital Signal Processing Methods. Springer, Cham. https://doi.org/10.1007/978-3-030-45359-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-45359-6_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45358-9

  • Online ISBN: 978-3-030-45359-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation