摘要自适应滤波器理论是自适应信号处理领域的一个分支，它能够自动地迭代调节自身的滤波器参数，以满足某种准则的要求，从而实现最优滤波。自适应滤波器由于收敛性和稳定性相对比较简单，而且已有相对比较完善的算法，已获得广泛应用。但目前的自适应滤波器的阶数一般都不可变，若滤波器的阶数太高，则不仅计算量增加，同时也增加了均方误差；若阶数太低，则无法满足滤波器的性能要求。而在许多自适应滤波器的应用场合，如信道估计或系统辨识等，系统的特征不可知或是时变的，固定长度的滤波器就可能无法达到最优性能。因此本论文将对如何能够得到滤波器的最优阶数进行探讨，介绍目前经典的三种变阶数最小均方算法（LMS）的思想及特点，并对他们的性能进行比较。其中基于分数阶数的变阶数LMS算法的性能和计算量均有较大的优势，然而该算法参数众多，在应用时很难选取获得最佳性能的参数，所以本文对参数的选取也给出了一定的讨论，并通过MATLAB仿真验证此方法的正确性。8505
关键词 自适应滤波器 变抽头长度 算法 MATLAB仿真
毕业设计说明书（论文）外文摘要
Title Order Optimization of the Adaptive Filter and Its Implementation techniques
Abstract
Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadwantage relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.
Keywords adaptive filters filter length tap-length variation
目 次
1 绪论 1
1.1、研究的背景及意义 1
1.2、国内外研究现状 2
1.3、自适应滤波原理 2
1.4、论文的安排 4
2 自适应滤波器的阶数优化原理及其实现技术 5
2.1、最优抽头长度及其代价函数 5
2.2、SF和GD算法的比较 6
2.3、本节小结 10
3 FT算法 11
3.1 算法分析 11
3.2 性能分析 13
3.3 算法统一 13
3.4 算法总结 14
4 FT算法参数选择依据 15
4.1 参数的理论选择 15
4.2 仿真参数对算法的影响 16
4.3 本节总结 20
结论 21
致谢 22 MATLAB自适应滤波器的阶数优化及其实现技术:http://www.751com.cn/tongxin/lunwen_6863.html