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Volterra filter identification, approximation, and equalization.

机译：Volterra滤波器的识别，近似和均衡。

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摘要

Volterra filters are a class of nonlinear digital filters based on polynomial mappings. Recently, Volterra filters have found application in important signal processing problems such as detection, estimation, nonlinear system identification, and adaptive filtering. This dissertation studies three important signal processing problems involving Volterra filters.; The first problem is the identification of the Volterra kernels of an unknown nonlinear system using measurements of the system input and output. Persistence of excitation conditions are established and several efficient algorithms are derived for identifying system parameters.; The second problem treated is the reduction of Volterra filter complexity. To this end, a tensor product basis approximation for the Volterra filter is proposed. Several design methods for such approximations and error bounds on their performance are given.; The last problem addressed is the equalization of nonlinear systems using Volterra filters. The equalization problem is analyzed theoretically using the Contraction Mapping Theorem. The analysis also incorporates response characteristics of the nonlinear system in order to improve the theoretical bounds on equalizer convergence.
机译：Volterra滤波器是一类基于多项式映射的非线性数字滤波器。最近，Volterra滤波器已发现可用于重要的信号处理问题，例如检测，估计，非线性系统识别和自适应滤波。本文研究了涉及Volterra滤波器的三个重要信号处理问题。第一个问题是使用系统输入和输出的测量结果来识别未知非线性系统的Volterra核。建立了激励条件的持久性，并导出了几种有效的算法来识别系统参数。解决的第二个问题是减少Volterra滤波器的复杂性。为此，提出了Volterra滤波器的张量积基近似。给出了几种在性能上近似和误差范围的设计方法。解决的最后一个问题是使用Volterra滤波器对非线性系统进行均衡。使用收缩映射定理从理论上分析均衡问题。该分析还结合了非线性系统的响应特性，以改善均衡器收敛的理论界限。

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  • 作者

    Nowak, Robert David.;

  • 作者单位

    The University of Wisconsin - Madison.;

  • 授予单位 The University of Wisconsin - Madison.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 1995
  • 页码 162 p.
  • 总页数 162
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

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