American Journal of Modeling and Optimization
ISSN (Print): 2333-1143 ISSN (Online): 2333-1267 Website: Editor-in-chief: Dr Anil Kumar Gupta
Open Access
Journal Browser
American Journal of Modeling and Optimization. 2013, 1(2), 11-18
DOI: 10.12691/ajmo-1-2-2
Open AccessArticle

Analysis of Identification Accuracy of Nonlinear System Based on Volterra Model in Frequency Domain

Vitaliy Pavlenko1 and Viktor Speranskyy2,

1ICS, Odessa National Polytechnic University, Odessa, Ukraine

2BEITI, Odessa National Polytechnic University, Odessa, Ukraine

Pub. Date: May 22, 2013

Cite this paper:
Vitaliy Pavlenko and Viktor Speranskyy. Analysis of Identification Accuracy of Nonlinear System Based on Volterra Model in Frequency Domain. American Journal of Modeling and Optimization. 2013; 1(2):11-18. doi: 10.12691/ajmo-1-2-2


The accuracy of the interpolation method for identification of nonlinear dynamical systems based on the Volterra model in the frequency domain is studied. To highlight the n–th partial component in the response of the system to the test signal the n–th partial derivative of the response using the test signal amplitude is found and its value is taken at zero. The polyharmonic signals are used as test ones. The algorithmic and software toolkit is developed for identification processes. This toolkit is used to construct the informational model of test system. The model is built as a first, second and third order amplitude–frequency characteristics and phase–frequency characteristics. The comparison of obtained characteristics with standard is given.

identification nonlinear dynamic systems volterra models multifrequency characteristics polyharmonic signals communication channels

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


Figure of 16


[1]  Giannakis, G.B., Serpedin, E. “A bibliography on nonlinear system identification and its applications in signal processing, communications and biomedical engineering”. Signal Processing – EURASIP, Elsevier Science B.V., 81(3), 2001, 533-580.
[2]  Westwick, D.T. Methods for the Identification of Multiple–Input Nonlinear Systems, Departments of Electrical Engineering and Biomedical Engineering, McGill University, Montreal, Quebec, Canada, 1995, 192-232.
[3]  Doyle, F.J, Pearson, R.K., Ogunnaike, B.A. Identification and Control Using Volterra Models. Published Springer Technology & Industrial Arts, 2001, 58-72.
[4]  Boyd, S., Jang, Y.S., Chua, L.O. “Measuring Volterra Kernels”. IEEE Trans. on Circuits and Systems, Vol. CAS-30, No.8, 1983, 571-578.
[5]  Peddanarappagari, K.V., Brandt-Pearce, M. “Volterra Series Approach for Optimizing Fiber–Optic Communications System Designs”. J. Lightwave Tech., 16 (11), 1998, 2046-2055.
[6]  Chang, K.F., Binh, L.N., Cambrell, G.K., Dabke, K.P. “Nonlinear frequency domain modeling of optical fibre transmission systems by Volterra series”. IOOC/OECC Conference, Sydney, July 2001, 360-362.
[7]  Pavlenko V.D. “Identification of Nonlinear Dynamic Systems in the Form of the Volterra Kernels on the Basis of the Data of Pulse Response Measurements”. Electronic Modeling, Vol. 32, №3, 2010, 3-18.
[8]  Pavlenko, V.D., Speranskyy, V.O. Identification of Nonlinear Dynamical Systems Using Volterra Model with Interpolation Method in Frequency Domain. Electrotechic and Computer Systems. № 05 (81), 2012, 229-234.
[9]  Schetzen, M. The Volterra and Wiener Theories of Nonlinear Systems. Wiley & Sons, New York, 1980, 321-360.
[10]  Pavlenko, V.D., Issa, S.I.M. “The Limitation of the choice frequencies test polyharmonic signals for the identification nonlinear system”. Proceedings of Odessa Polytechnic University, Ukraine, 1 (31), 2008, 107-113.
[11]  Goswami, J.G., Chan, A.K. Fundamentals of Wavelets: Theory, Algorithms, and Applications. Publishing John Wiley & Sons, Inc., 1999, 125-137.
[12]  Danilov, L.V., Mathanov, P.N., Philipov, E.S. The theory of nonlinear electrical circuits. Published Energoatomizdat, Leningrad, 1990, 136-148.
[13]  Pavlenko, V.D., Speranskyy, V.O. “Communication Channel Identification in Frequency Domain Based on the Volterra Model”. Proceedings of the International Conference on Computers, Digital Communications and Computing (ICDCC'11), Barcelona, Spain, September 15-17, 2011. Published by WSEAS Press, 2011, 218-222.