Statistical-Mechanical Analysis of the Second-Order Adaptive Volterra Filter

机译：二阶自适应Volterra滤波器的统计力学分析

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The Volterra filter is a digital filter that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system based on the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form that describe the behaviors of the macroscopic variables and obtain the exact solution by solving them analytically. In addition, the validity of the derived theory is confirmed by comparison with numerical simulations.

机译：Volterra滤波器是可以描述非线性的数字滤波器。在本文中，我们通过统计力学方法分析了基于Volterra滤波器的自适应信号处理系统的动态行为。在假定抽头延迟线无限长时的自平均基础上，我们以确定性和封闭形式导出联立微分方程，这些微分方程描述了宏观变量的行为，并通过解析求解来获得精确解。另外，通过与数值模拟的比较证实了推导理论的有效性。

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《Asia-Pacific Signal and Information Processing Association Annual Summit and Conference》|2018年|1821-1824|共4页
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Kimiko Motonaka; Takashi Katsube; Yoshinobu Kajikawa; Seiji Miyoshi;
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Adaptive systems; Numerical simulation; Differential equations; Noise measurement; Kernel; Signal processing algorithms; Symmetric matrices;

机译：自适应系统;数值模拟;微分方程;噪声测量;核;信号处理算法;对称矩阵;

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专利

1. Adaptive second-order Volterra filtering and its application to second-order drift phenomena [J] . Kiho Kim, Sung Bae Kim IEEE Journal of Oceanic Engineering . 1994,第2期

机译：自适应二阶Volterra滤波及其在二阶漂移现象中的应用
2. An LMS adaptive second-order Volterra filter with a zeroth-order term: steady-state performance analysis in a time-varying environment [J] . Sayadi M., Fnaiech F. IEEE Transactions on Signal Processing . 1999,第3期

机译：具有零阶项的LMS自适应二阶Volterra滤波器：时变环境中的稳态性能分析
3. Design of quaternion-valued second-order Volterra adaptive filters for nonlinear 3-D and 4-D signals [J] . Engin Cemal Menguec Signal processing . 2020,第Sepa期

机译：用于非线性3-D和4-D信号的四元数值二阶Volterra自适应滤波器的设计
4. Statistical-Mechanical Analysis of the Second-Order Adaptive Volterra Filter [C] . Kimiko Motonaka, Takashi Katsube, Yoshinobu Kajikawa, Asia-Pacific Signal and Information Processing Association Annual Summit and Conference . 2018

机译：二阶自适应Volterra滤波器的统计 - 力学分析
5. Slider Crank Wave Energy Converter Performance Analysis with Adaptive Autoregressing Filtering [D] . Khan, Md. Rakib Hasan. 2019

机译：具有自适应自动归档滤波的滑块曲柄波能量转换器性能分析
6. Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering [O] . Jianbo Gao, Jing Hu, Wen-wen Tung 2011

机译：促进联合混沌并通过非线性自适应生物信号分形分析
7. INPUT SIGNAL DECORRELATION APPLIED TO ADAPTIVE SECOND-ORDER VOLTERRA FILTERS IN THE TIME DOMAIN [O] . Fabian Kuech, Marcus Zeller, Walter Kellermann 2009

机译：输入信号解耦应用于时域中的自适应二阶Volterra滤波器
8. Analysis of the Howells-Applebaum Algorithm in the Presence of Moving Interference. The Use of Lattice Filters in Adaptive Array Processors. Stability Analysis of LMS Adaptive Filters. Adaptive Array Processors with Moving Interference. [R] . Tuteur, F. B. 1982

机译：移动干扰下的Howells-applebaum算法分析。格子滤波器在自适应阵列处理器中的应用。 Lms自适应滤波器的稳定性分析。具有移动干扰的自适应阵列处理器。

Statistical-Mechanical Analysis of the Second-Order Adaptive Volterra Filter

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