Abstract
Assessing the nonlinearity of one signal, system, or dependence of one signal on another is of great importance in the design process. The article proposes an algorithm for simplified nonlinearity estimation of digital signals. The solution provides detailed information to constructors about existing nonlinearities, which in many cases is sufficient to make the correct choice of processing algorithms. The programming code of the algorithm is presented and its implementation is demonstrated on a set of basic functions. Several steps to further development of the proposed approach are outlined.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Haykin, S.: Signal processing in a nonlinear, nongaussian, and nonstationary world. In: Chollet, G., Esposito, A., Faundez-Zanuy, M., Marinaro, M. (eds.) NN 2004. LNCS (LNAI), vol. 3445, pp. 43–53. Springer, Heidelberg (2005). https://doi.org/10.1007/11520153_3
Xiong, X.Y.Z., Jiang, L.J., Schutt-Aine, J.E., Chew, W.C.: Volterra series-based time-domain macromodeling of nonlinear circuits. IEEE Trans. Compon. Packag. Manuf. Technol. 7(1), 39–49 (2017). https://doi.org/10.1109/TCPMT.2016.2627601
Roweis, S.T., Ghahramani, Z.: Learning nonlinear dynamical system using the expectation-maximization algorithm. In Haykin, S. (ed.) Kalman Filtering and Neural Networks, First published: 01 October 2001. Wiley, Hoboken (2001). https://doi.org/10.1002/0471221546.ch6, https://cs.nyu.edu/~roweis/papers/nlds.pdf
Bar-Shalom, Y., Forthmann, T.: Tracking and Data Association. Academic Press, San Diego (1988)
Bar-Shalom, Y. (ed.): Multitarget-Multisensor Tracking: Advanced Applications. Norwood, Chicago (1990)
Bar-Shalom, Y., Li, X.R.: Multitarget-Multisensor Tracking: Principles and Techniques. Artech House, Boston (1993)
Li, X.R.: Engineers’ Guide to Variable-Structure Multiple-Model Estimation and Tracking (2000). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.61.8701&rep=rep1&type=pdf
Blom, H.A.P., Bloem, E.A.: Joint IMM and coupled PDA to track closely spaced targets and to avoid track coalescence. In: Proceedings of the Seventh International Conference on Information Fusion, pp. 130–137 (2005)
Beale, E.M.L.: Confidence regions in non-linear estimation. J. Roy. Stat. Soc. Ser. B (Methodol.) 22(1), 41–88 (1960)
Desoer, C.A., Wang, Y.T.: Foundations of feedback theory for nonlinear dynamical systems. IEEE Trans. Circ. Syst. 27(2), 104–123 (1980)
Bates, D.M., Watts, D.G.: Relative curvature measures of nonlinearity. J. Roy. Stat. Soc.: Ser. B (Methodol.) 42(1), 1–25 (1980). Wiley for the Royal Statistical Society. https://www.jstor.org/stable/2984733
Emancipator, K., Kroll, M.H.: A quantitative measure of nonlinearity. Clin. Chem. 39(5), 766–772 (1993)
Tugnait, J.K.: Testing for linearity of noisy stationary signals. IEEE Trans. Signal Process. 42(10), 2742–2748 (1994)
Allgower, F.: Definition and Computation of a Nonlinearity Measure. IFAC Nonlinear Control Systems Design, Tahoe City, California, USA (1995)
Helbig, A., Marquardt, W., Allgower, F.: Nonlinearity measures: definition, computation and applications. J. Process Control 10, 113–123 (2000)
Barnett, A.G., Wolff, R.C.: A time-domain test for some types of nonlinearity. IEEE Trans. Signal Process. 53(1), 26–33 (2005)
Hosseini, S.M., Johansen, T.A., Fatehi, A.: Comparison of nonlinearity measures based on time series analysis for nonlinearity detection. Model. Identif. Control 32(4), 123–140 (2011). ISSN 1890-1328
Haber, R.: Nonlinearity test for dynamic process. In: IFAC Identification and system Parameter Estimation (1985)
Smith, R.: A mutual information approach to calculating nonlinearity. The ISI’s Journal for the Rapid Dissemination of Statistics Research. https://doi.org/10.100X/sta.0000, (http://wileyonlinelibrary.com)
Liu, Y., Li, X.R.: Measure of nonlinearity for estimation. IEEE Trans. Signal Process. 63(9), 2377–2388 (2015)
Shi, W., Cheung, C.: Performance evaluation of line simplification algorithms for vector generalization. Cartographic J. 43(1), 27–44 (2006)
Kotchoni, R.: Detecting and measuring nonlinearity. MDPI, Econometrics 6, 37 (2018). https://doi.org/10.3390/econometrics6030037
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Alexiev, K. (2020). Nonlinearity Estimation of Digital Signals. In: Simian, D., Stoica, L. (eds) Modelling and Development of Intelligent Systems. MDIS 2019. Communications in Computer and Information Science, vol 1126. Springer, Cham. https://doi.org/10.1007/978-3-030-39237-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-39237-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39236-9
Online ISBN: 978-3-030-39237-6
eBook Packages: Computer ScienceComputer Science (R0)