Identifying odd/even-order binary kernel slices for a nonlinear system using inverse repeat m-sequences. Hu JY, Yan G, Wang T - Comput Math Methods Med (2015) Bottom Line: 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.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. View Article: PubMed Central - PubMed Affiliation: School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China. ABSTRACTThe 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. Show MeSH MajorComputer Simulation*Nonlinear Dynamics*MinorAlgorithmsComputational BiologyNormal DistributionSoftwareSystems Biology Related in: MedlinePlus © Copyright Policy Related In: Results  -  Collection License getmorefigures.php?uid=PMC4385604&req=5 .flowplayer { width: px; height: px; } fig2: Weiner model representing a general nonlinear dynamic system in cascade form. Mentions: A general nonlinear dynamic system can be represented by a Wiener model consisting of two subsystems in cascade form [24]. This system consists of a dynamic linear subsystem g[n] followed by a static nonlinear subsystem m[·], as shown in Figure 2. The output of the dynamic subsystem g[·] is (28)vn=∑k=0M−1xkgn−k,where M represents the memory length of the system.

Identifying odd/even-order binary kernel slices for a nonlinear system using inverse repeat m-sequences.

Hu JY, Yan G, Wang T - Comput Math Methods Med (2015)

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fig2: Weiner model representing a general nonlinear dynamic system in cascade form.
Mentions: A general nonlinear dynamic system can be represented by a Wiener model consisting of two subsystems in cascade form [24]. This system consists of a dynamic linear subsystem g[n] followed by a static nonlinear subsystem m[·], as shown in Figure 2. The output of the dynamic subsystem g[·] is (28)vn=∑k=0M−1xkgn−k,where M represents the memory length of the system.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

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

ABSTRACT
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.

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