自适应子带仿射投影算法研究

发布时间：2018-03-18 19:21

本文选题：自适应滤波　切入点：子带自适应滤波算法　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：从上世纪八十年代至今,数字信号处理相关技术发展迅速,这得益于越来越多的实用性技术可被应用于基于数字信号处理的一系列算法当中。在面对一些统计特性未知的信号时,传统的基本算法并不能有效地对一些复杂信号进行处理分析,解决的一种方法则是通过自适应滤波器,优化内部参数来改变滤波器本身特性,而自适应滤波算法在信号处理应用中必不可少。自适应滤波器在回声消除,主动噪声控制等系统辨识领域应用广泛。基本的最小均方(LMS)算法因为结构简单,计算复杂度低等优点被广泛运用,但对于高相关性的输入信号,LMS滤波器则会出现收敛速度变慢,梯度噪声被放大等问题。为解决该类问题,仿射投影算法(APA)和子带自适应滤波(SAF)算法相继被提出。为优化收敛速度和稳态失调性能,本文在APA和SAF相结合的基础上做出改进,并利用变步长和成比例思想进一步提升新算法的跟踪能力。首先,简要对传统的AP算法、归一化子带自适应滤波(NSAF)算法及其改进算法的基本思想做出概括。然后分析了现有的NSAF算法及其改进算法各自的优缺点。当输入端为有色信号时,尤其是在高背景噪声环境中,针对改进的多带结构子带自适应滤波算法(IMSAF)跟踪能力下降等的问题,本文提出一种改进的仿射投影子带自适应滤波(IAPSAF)算法,为进一步说明所提算法的有效性,对新算法进行了稳态分析。其次,当输入信号为相关信号时,NSAF在收敛速度上确实比归一化最小均方(NLMS)算法快很多,且计算复杂度上两者较为接近,尤其是在长脉冲响应中。基于这个特性,语音回声消除(AEC)成为NSAF的一个重要应用。然而,由于固定步长的使用,NSAF需要解决所存在的快收敛速度和低稳态失调的折中问题,受益于凸组合的思想,本文在IAPSAF基础上提出了一种组合步长的仿射投影子带自适应滤波(CSS-IAPSAF)算法,相比于凸组合算法,该算法不再需要两个滤波器进行更新,并且计算复杂度有所降低。最后,在回声消除中,针对具有稀疏特性的脉冲响应,Duttweiler在2000年提出成比例归一化最小均方(Proportionate NLMS)算法,基本思想就是根据每个抽头权系数增益参数的不同,按照数值大小成比例进行更新,使该算法在回声消除应用中获得较快的收敛速度和较低的稳态失调。在输入信号呈现相关性较高特性时,成比例归一化子带自适应(PNSAF)算法也表现出较快的收敛速度,基于这一思想,同时为了进一步改善在稀疏脉冲响应时IAPSAF的性能,本文提出了一种改进的成比例APSAF(IP-APSAF)算法,同时和其他改进成比例算法进行比较,不但有提升了收敛速度,同时较低稳态失调。通过在MATLAB软件中所做的仿真实验,验证了本文所提出的各种改进仿射投影子带自适应滤波算法的有效性。
[Abstract]:Since -20s, digital signal processing technology has developed rapidly. This is due to the fact that more and more practical techniques can be applied to a series of algorithms based on digital signal processing. The traditional basic algorithm can not effectively process and analyze some complex signals. One way to solve the problem is to change the characteristics of the filter by adaptive filter and optimize the internal parameters. Adaptive filter is necessary in signal processing. Adaptive filter is widely used in system identification such as echo cancellation, active noise control and so on. The basic minimum mean square (LMS) algorithm is simple because of its simple structure. The advantages of low computational complexity are widely used, but for the high correlation input signal LMS filter, the convergence rate will slow down, gradient noise will be amplified and so on. Affine projection algorithm (APA) and subband adaptive filter (SAF) algorithm have been proposed one after another. In order to optimize the convergence rate and steady-state misalignment performance, this paper makes an improvement based on the combination of APA and SAF. And the idea of variable step size and proportionality is used to further improve the tracking ability of the new algorithm. Firstly, the traditional AP algorithm is briefly introduced. The basic ideas of the normalized subband adaptive filter (NSAF) algorithm and its improved algorithm are summarized. Then, the advantages and disadvantages of the existing NSAF algorithm and its improved algorithm are analyzed. When the input is a colored signal, especially in a high background noise environment, In this paper, an improved affine projection subband adaptive filter (IAPSAF) algorithm is proposed to further illustrate the effectiveness of the proposed algorithm. The steady state analysis of the new algorithm is given. Secondly, when the input signal is a correlation signal, the convergence speed of NSAF is much faster than that of the normalized minimum mean square (NLMS) algorithm, and the computational complexity is close. Especially in long pulse response. Based on this characteristic, speech echo cancellation has become an important application of NSAF. However, due to the use of fixed step size, it is necessary to solve the problems of fast convergence rate and low steady state misalignment. This paper presents an affine projection subband adaptive filter CSS-IAPSAF algorithm based on IAPSAF. Compared with the convex combination algorithm, the algorithm no longer needs two filters to update. And the computational complexity is reduced. Finally, in echo cancellation, a proportional normalized least mean square (LMS) algorithm is proposed in 2000 for pulse response with sparse characteristics. The basic idea is to update it in proportion to the magnitude of each tap weight coefficient gain parameter. The proposed algorithm can obtain faster convergence speed and lower steady-state misalignment in echo cancellation applications. When the input signal presents high correlation, the proportional normalized sub-band adaptive PNSAF algorithm also exhibits a faster convergence rate. Based on this idea, and in order to further improve the performance of IAPSAF in sparse impulse response, an improved proportional APSAF IP-APSAF algorithm is proposed, which is compared with other improved proportional algorithms. At the same time, the low steady-state misalignment. The effectiveness of the improved affine projection subband adaptive filtering algorithm is verified by the simulation experiments in MATLAB software.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7;TN713

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