Applications of NIMRAD in Electrochemistry

  • Raoul R. Nigmatullin
  • Paolo Lino
  • Guido Maione


This chapter shows how to combine the methods outlined in the previous chapters for application to electrochemistry. The first adopted method, which can be considered as original, is based on the ideas of Yu. Babenko, who generalised the Pythagorean theorem for a wide class of geometrical figures with high symmetry. By applying this method is possible to find some discrete geometrical invariants (DGI) in random sequences to identify deterministic and quantitative parameters inside the measured data, which can represent a universal platform for comparing random sequences, one with each other. An example illustrates the procedure for the treatment of electrochemical measurements, which can be generalised for the quantitative reading of other random functions. Another approach derives from the combination of the modified Fourier transform and the generalised principal component analysis (GPCA), which enables, in some cases, a more detailed data analysis. The third method is associated with the generalisation of the quasi-periodic processes on fractal objects. If one considers the self-similar/fractal processes, then it is possible to create the fractal theory of percolation, which can find confirmation from the analysis on real data. The reader will find this theory rather efficient for application to other fractal objects where is possible to observe similar percolation phenomena.


DGI-method The generalisation of the PCA The test of the DGI-method on electrochemical data Fractal theory of percolation 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Raoul R. Nigmatullin
    • 1
  • Paolo Lino
    • 2
  • Guido Maione
    • 2
  1. 1.Radioelectronics and Informative-Measurement Technics DepartmentKazan National Research Technical University named by A.N. Tupolev (KNRTU-KAI)KazanRussia
  2. 2.Department of Electrical and Information EngineeringPolytechnic University of BariBariItaly

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