一種新的快速最小平均平方誤差的Volterra適應演算法

A Fast LMS Second-Order Volterra Filtering Algorithm

許世澤(Shih-Tse Hsu)

指導教授 ： 李仲溪

元智大學/工程學院/電機與資訊工程研究所/碩士(1998年)

摘要

我們發展了一種新的快速LMS的Volterra適應演算法。此種演算法是由取樣處理的LMS演算法等效推導來的，因此保留了相同的特性。與一般區塊處理方法不同的是，此種快速演算法在小區塊長度時亦可降低運算量。而一般的區塊處理方法要使用在較大的區塊長度下才能降低運算量，同時大的區塊長度需佔用較大的記憶體以及會形成較長的系統延遲。另外，考慮到在運算量與效能之間做取捨，我們分別從簡化濾波器以及簡化一個訊號相關矩陣來做近似的實現。

關鍵字

Volterra ； 最小平均平方誤差 ； 快速有限脈衝響應

並列摘要

In this thesis, we present a block formulation of least mean square (LMS) adaptive Volterra filter. This formulation has a mathematical equivalence with time domain sample-processing LMS. Hence, it maintains the same performance while allowing a reduction in arithmetical complexity (even for small block size). Simulation results are presented to validate the usefulness of our algorithm. We also consider several alternatives to trade performance with complexity.

並列關鍵字

Volterra ； LMS ； fast FIR

參考文獻

[1] J. Benesty and P. Duhamel, "A fast exact least mean square adaptive algorithm," IEEE Transactions on Signal Processing, Vol. 40, No. 12, pp. 2904-2920, Dec. 1992.

[3] P. M. Clarkson and M. V. Dovic, "Stability and convergence behaviour of second-order LMS Volterra filter," Electronics Letters, Vol. 27, No. 5, pp. 441-443, Aug. 1991.

[6] S. Im and E. J. Powers, "A block LMS algorithm for third-order frequency-domain Volterra filters," IEEE Signal Processing Letters, Vol. 4, No. 3, pp. 75-78, March 1997.

[7] J. Lee and V. J. Mathews, "A fast recursive least square adaptive second-order Volterra filter and its performance analysis," IEEE Transactions on Signal Processing, Vol. 41, No. 3, pp. 1087-1102, March 1993.

[8] V. J. Mathews, "Adaptive polynomial filters," IEEE Signal Processing Magazine, Vol. 8, pp. 10-26, July 1991.