Performance Analysis of Delayless Subband Adaptive Filter

自适应滤波器在电子、通信和主动噪声控制等领域得到了广泛的研究。近年来，子带自适应滤波器在一些应用中得到了应用。传统子带自适应滤波器的输出信号中存在传输延迟。这种延迟是声回波消除和主动噪声控制应用中的一个大问题。最近，Morgan和Thi提出了一种无延迟子带自适应滤波器。然而，该方案的分析是定性的，不完整的。同时，该方案需要大量的计算量。本研究的目的是对无延迟方案进行定量分析，并提出一种较优的方法。得到了以下结果：(a)常规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转换得到的。说明了这种转换在传统的无延迟方案中是奇异的。变换矩阵不是满秩的，因此最优Wiener解不属于它的值域空间。(b)利用Hadamard变换的新方法针对具有2^m子带的子带无延迟自适应方案，提出了利用Hadamard变换的新方法。结果表明，在2波段情况下，可以避免上述缺陷。从子带滤波器到全带滤波器的分接转换可以快速执行，因为阿达玛变换不需要乘法运算。(c)投影法提高了收敛速度，当该方法与自适应算法（如NLMS）结合使用时，收敛速度可能会降低。采用投影法可以提高算法的收敛速度。仿真结果证明了这种效应。

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.