二阶自适应IIR陷波器复数算法的收敛性分析.pdf

第20 卷第1 期 系 统 仿 真 学 报© Vol. 20 No. 1 2008 年1 月 Journal of System Simulation Jan., 2008 二阶自适应IIR 陷波器复数算法的收敛性分析 侯颜平，梁 红 （西北工业大学航海学院，西安 710072 ） 摘 要：针对背景噪声中复正弦信号的检测和估计问题，分析了自适应格型IIR 陷波器的两种复数 算法即梯度算法和简化的梯度算法的收敛性能，证明了输入白噪声方差的大小不影响收敛速度。并 分析了由一阶自回归模型产生的有色噪声对算法的收敛性能的影响，为有色噪声中复正弦信号检测 的自适应过程的参数的选取提供了理论依据。 关键词：IIR 陷波器；白噪声；有色噪声；自适应算法 中图分类号：TN911.7 文献标识码：A 文章编号：1004-731X (2008) 01-0037-03 Convergence Analysis of Complex Adaptive Second-order IIR Notch Filters HOU Yan-ping, LIANG Hong (College of Marine, Northwestern Polytechnical University, Xi’an 710072, China) Abstract: A complex algorithm of gradient-based second-order adaptive IIR notch filter was proposed, and the convergence characteristics about gradient algorithm and simplified algorithm were investigate. It shows that the convergence speed does not depend on the variance of input white noise; and the simplified algorithm converges faster than the gradient algorithm. At the same time, the effects of colored input noise generated by first-order autoregressive model to the convergence speed were proposed . The theoretical analyses show that the initialization of the adaptive process is related with convergence speed in colored noise. The results of computer simulation are shown which confirm the theoretical prediction. Key words: IIR notch filter; white noise; colored noise; adaptive algorithm 1 为复高斯随机变量，n(k ) ＝n (k )