Performance Analysis of Delayless Subband Adaptive Filter

自适应滤波器的研究在电子、通信、有源噪声控制等领域得到了广泛的应用。近年来，子带自适应滤波器已被用于一些应用。在传统的子带自适应滤波器的输出信号中出现传输延迟。这种延迟在声学回声消除器和有源噪声控制的应用中是一个大问题。最近，Morgan和Thi提出了一种无延迟子带自适应滤波器。然而，对该计划的分析是定性的，不完整。此外，该方案需要大量的计算。本研究的目的是对无延迟方案进行定量分析，并发展出一种上级方法。取得了以下结果。(a)传统无延迟自适应滤波器的定量分析无延迟方案中的全带自适应滤波器是通过对各子带滤波器的抽头进行变换而得到的。它是澄清，这种转换在传统的无延迟计划是奇异的。转换矩阵不是满秩的，因此最优Wiener解不属于其值域空间。(b)提出了一种新的基于Hadamard变换的自适应方案，该方案适用于具有2.m个子带的子带无时延自适应方案。结果表明，上述缺陷是避免了2带的情况下。从子带滤波器到全带滤波器的抽头转换可以快速执行，因为Hadamard变换不需要乘法运算。(c)通过投影方法提高收敛速度当所提出的方法与诸如NLMS的自适应算法一起用于某些应用时，收敛速度可能降低。采用投影法可以提高收敛速度。通过一些模拟证明了这种效果。

The researches of adaptive filters have been done in the some fields such as electronics, communication and active noise control. In recent years, a subband adaptive filter has been used for some applications. A transmission delay appears in the output signal of a conventional subband adaptive filter. This delay is a big problem in the application of an acoustic echo canceler and an active noise control. Recently, a delayless subband adaptive filter has been proposed by Morgan and Thi. However the analysis of the scheme is qualitative and not complete. Also, this scheme require a large amount of computations. The aim of this research is to analyze the delayless scheme quantitatively and to develop a superior method. The following results have been obtained.(a) quantitative analysis of the conventional delayless adaptive filterThe fuilband adaptive filter in the delayless scheme is obtained by the conversion of the taps of each subband filter. It is clarified that this conversion in the conventional delayless scheme is singular. The conversion matrix is not of full-rank so that the optimal Wiener solution does not belong to its range space.(b) new method with using the Hadamard transformA new method using the Hadamard transform is proposed for the subband delayless adaptive scherne with 2^m subbands. It is demonstrated that the above defect is avoided for the 2-band case. The tap conversion from subband filters to a fullband filter can be performed fast because the Hadamard transform does not require multiplication operations.(c) improvement of the convergence speed by the projection methodWhen the proposed method is used in some application with an adaptive algorithm such as NLMS, a convergence speed may decrease. The convergence speed can be improved by using the projection method. This effect is demonstrated by some simulations.