一种可变步长傅里叶分析器的统计特性分析

doi:10.3969/j.issn.0372-2112.2015.09.013

电子学报 ›› 2015, Vol. 43 ›› Issue (9): 1763-1769.DOI: 10.3969/j.issn.0372-2112.2015.09.013

一种可变步长傅里叶分析器的统计特性分析

温良^1,2, 黄博妍¹, 魏国¹, 孙金玮¹, 沈毅¹

1. 哈尔滨工业大学自动化测试与控制系, 黑龙江哈尔滨 150001;
2. 96361部队, 青海西宁 810000

收稿日期:2014-06-03 修回日期:2015-06-14 出版日期:2015-09-25
- 通讯作者:
- 黄博妍
- 作者简介:
- 温良男,1984年生于黑龙江鸡西,任职于中国人民解放军96361部队.哈尔滨工业大学电气工程及自动化学院在读博士研究生.研究方向为自适应信号处理、主动噪声控制.E-mail:lwen@hit.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61171183,No.61471140); 中央高校基本科研业务费专项资金 (No.HIT.IBRSEM.201306,No.HIT.NSRIF.201614)

Statistical Analysis for a Variable Step-Size Fourier Analyzer

WEN Liang^1,2, HUANG Bo-yan¹, WEI Guo¹, SUN Jin-wei¹, SHEN Yi¹

1. Department of Automatic Test and Control, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China;
2. 96361 PLA Troops, Xining, Qinghai 810000, China

Received:2014-06-03 Revised:2015-06-14 Online:2015-09-25 Published:2015-09-25
- Supported by:
- National Natural Science Foundation of China (No.61171183, No.61471140); Fundamental Research Funds for the Central Universities (No.HIT.IBRSEM.201306, No.HIT.NSRIF.201614)

摘要/Abstract

摘要：

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.

关键词: 自适应傅里叶分析器, 可变步长最小均方算法, 统计特性分析, 追踪性能, 收敛性

Abstract:

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.

Key words: adaptive Fourier analyzer, variable step-size least mean square (VSS-LMS), statistical analysis, tracking capability, convergence

中图分类号:

TB535

温良, 黄博妍, 魏国, 等. 一种可变步长傅里叶分析器的统计特性分析[J]. 电子学报, 2015, 43(9): 1763-1769.

WEN Liang, HUANG Bo-yan, WEI Guo, et al. Statistical Analysis for a Variable Step-Size Fourier Analyzer[J]. Acta Electronica Sinica, 2015, 43(9): 1763-1769.

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一种可变步长傅里叶分析器的统计特性分析

Statistical Analysis for a Variable Step-Size Fourier Analyzer

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