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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 454638, 9 pages
Research Article

Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China

Received 27 June 2014; Revised 9 September 2014; Accepted 1 October 2014

Academic Editor: Shengyong Chen

Copyright © 2015 Jin-yan Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method.