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，子带自适应滤波器在一些领域得到了应用。传输延迟出现在常规子带自适应滤波器的输出信号中。这种延迟是声学回声消除器和有源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，对该方案的分析是定性的，也是不完整的。此外，该方案需要大量的计算量。本研究的目的是对无延误方案进行定量分析，并开发出一种更好的方法。(A)常规无延迟自适应滤波器的定量分析无延迟方案中的频带自适应滤波器是通过每个子带滤波器的抽头转换而得到的。阐明了传统的无延迟格式中的这种转换是奇异的。变换矩阵不是满秩阵，因此最优维纳解不属于其值域空间。(B)针对子带为2^m个子带的无延迟自适应分集，提出了一种基于Hadamard变换的新方法。结果表明，对于双频段情况，上述缺陷是可以避免的。由于Hadamard变换不需要乘法运算，因此子带滤波到全带滤波的抽头变换可以快速完成。(C)用投影法提高收敛速度。当所提出的方法用于某些应用时，如NLMS自适应算法，收敛速度可能会降低。采用投影法可以提高收敛速度。一些仿真实验证明了这一效果。

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.