Analysis of subband adaptive filters and minor component extraction algorithms by using the averaging method

子带自适应滤波器和平均法次要成分提取算法分析

• 批准号: 12650443
• 负责人: SAKAI Hideaki
• 金额: $ 1.22万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12650443/
• 关键词: subband adaptive filter; minor component analysis; averaging method; ODE method; deflation technique; Lyapunov equation; マルチレートシステム; デフレーション

Since a system of subband adaptive filters includes some decimators and an analysis filter bank, it is difficult to examine some properties of the system by directly applying the averaging method to the system in the time domain. Therefore we developed a new analysis method in which the averaging method was applied to the frequency domain expression of the algorithm converted by the discrete Fourier transform. We applied this analysis method to both the delay-less subband adaptive filter (DLSADF) with Hadamard transform and the new structure of subband adaptive filter (SADF) proposed by Pradhan and Reddy. As a result, the following properties have been obtained.1. The stability condition of the DLSADF with Hadamard transform is derived. A mode that causes the slow convergence of the algorithm is found out.2. A formula that evaluates the variance of the error signal in the DLSADF with Hadamard transform is theoretically derived.3. By applying the same method to the Pradhan's SADF, it is shown that the algorithm is always stable and that the variance of the error signal is less than that of the conventional fullband adaptive filter.Also, we proposed a new algorithm to extract multiple minor components. The proposed algorithm was derived by combining a single minor component extraction algorithm proposed by Douglas et al. with the deflation technique and the Gram-Schmidt orthogonalization. By applying the ODE method to the proposed method, the following results have been obtained1. The proposed algorithm is always stable.2. The covariance matrix of the extracted minor components is evaluated. Then it is required to solve the Lyapunov equation. In this process, some indeterminate terms appear so that we introduce some appropriate constraints to obtain the solution.All the above results were summarized and have been submitted to international journals.

由于一个子带自适应滤波系统包括一些抽取器和一个分析滤波器组，因此很难直接将平均法应用到系统的时间域中来检验系统的某些特性。因此，我们提出了一种新的分析方法，将平均法应用于离散傅里叶变换后的算法的频域表示。我们将这种分析方法应用于基于Hadamard变换的无时延子带自适应滤波器(DLSADF)和Pradhan和Reddy提出的子带自适应滤波器(SADF)的新结构。结果，获得了以下性质1。推导了基于Hadamard变换的DLSADF的稳定性条件。找出了导致算法收敛缓慢的一种模式。从理论上推导了用阿达玛变换计算DLSADF中误差信号方差的公式。将同样的方法应用于Pradhan的SADF，证明了该算法是稳定的，并且误差信号的方差小于传统的全带自适应滤波器，同时提出了一种新的提取多个次要分量的算法。该算法结合了Douglas等人提出的单一次要成分提取算法。利用收缩技术和Gram-Schmidt正交化。将常微分方程方法应用于所提出的方法，得到了以下结果1。提出的算法始终是稳定的。估计提取的次要分量的协方差矩阵。然后需要求解李亚普诺夫方程。在这个过程中，出现了一些不确定项，因此我们引入了一些适当的约束条件来获得解。

项目成果

Hideaki Sakai: "Stabilisation of fast QRD inverse-updates adaptive filtering algorithm"IEE Proc. Vision, Image Signal Processing. Vol.148, No.2. 107-114 (2001)

Hideaki Sakai：“快速 QRD 逆更新自适应滤波算法的稳定性”IEE Proc。

S. Miyagi and H. Sakai: "Convergence analysis of The delayless subband adaptive filter based on the frequency domain expression"Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing 2000. Vol. 1. 368-371 (2000)

S. Miyagi 和 H. Sakai：“基于频域表达式的无延迟子带自适应滤波器的收敛性分析”Proc。

Shigeyuki Miyagi: "Performance Comparison between the Filtered-Error and the Filtered-X LMS Algorithm"Proc. of ISCAS2001, Sydney, Australia. Vol.II. 661-664 (2001)

Shigeyuki Miyagi：“Filtered-Error 和 Filtered-X LMS 算法之间的性能比较”Proc。

Hideaki Sakai: "Stabilisation of fast QRD inverse-updates adaptive filtering algorithm"IEE Proc. Vision, Image Signal Processing. Vol.148 NO.2. 107-114 (2001)

Hideaki Sakai：“快速 QRD 逆更新自适应滤波算法的稳定性”IEE Proc。

Hideaki Sakai: "Performance analysis of an adaptive algorithm for minor component analysis"Proc. of X European Signal Processing Conference. Vol.2. 853-856 (2000)

Hideaki Sakai：“次要成分分析自适应算法的性能分析”Proc。