一种可变步长傅里叶分析器的统计特性分析

可变步长最小均方(Variable step-size LMS,VSS-LMS)算法的傅里叶分析器在稳态误差、收敛速度及追踪能力方面具有优异性能,对其进行全面的统计特性分析具有重要意义.本文基于误差服从高斯分布等假设在平均及均方意义下,推导出描述系统动态特性的差分方程组,完成系统的动态数学建模,进而对系统进行稳态性能分析,给出系统稳态误差关于参考信号频率、系统参数和附加噪声的表达式,为系统应用中的参数选取提供有效指导.仿真表明,本文建立的统计模型与仿真结果具有一致性,验证了分析的有效性.

Statistical Analysis for a Variable Step-Size Fourier Analyzer

Fourier analyzer,based on variable step-size least mean square (LMS) algorithm,enjoys fast convergence,good tracking capability and small steady state errors.Thus,a thorough statistical analysis of the Fourier analyzer is of great significance.In this paper,differential equations governing the dynamic of the system are derived in the mean and mean square sense on the premise that the error signals obey Gauss distribution.Closed-form expressions indicating relationships of steady-state error,reference signal frequencies,system parameters and addictive noise are carried out for steady-state performance analysis,which can serve as the fundamental principle for system parameter selection.Numerous simulations confirm the validity of the analytical findings.