Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm
Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm
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DOI：
10.1587/transfun.2021eap1013
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
K. Motonaka;Tomoya Koseki;Y. Kajikawa;S. Miyoshi
中科院分区：
文献类型：
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作者：
K. Motonaka;Tomoya Koseki;Y. Kajikawa;S. Miyoshi
Volterra滤波器是一种能够描述非线性的数字滤波器。本文用统计力学方法分析了包含Volterra滤波器的自适应信号处理系统的动态行为。基于抽头延迟线假定为无穷长时所具有的自平均性质，我们导出了描述宏观变量行为的确定性和闭合形式的微分方程组。通过对方程的解析求解，我们得到了精确解。此外，通过与数值模拟的比较，验证了理论推导的正确性。关键词：Volterra滤波、自适应滤波、统计-机械信息学、LMS算法
The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations. key words: Volterra filter, adaptive filter, statistical-mechanical informatics, LMS algorithm