基于Kaiser窗的分数阶Fourier变换与时频分析  

Fractional Fourier transform based Kaiser window and time⁃frequency analysis

作　　者：卢恋 任伟新 王世东 LU Lian;REN Wei-xin;WANG Shi-dong(School of Civil and Hydraulic Engineering,Hefei University of Technology,Hefei 230009,China;Key Laboratory for Resilient Infrastructures of Coastal Cities,Ministry of Education,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009 [2]深圳大学滨海城市韧性基础设施教育部重点实验室,广东深圳518060

出　　处：《振动工程学报》2023年第3期698-705,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51778204);深圳市科创委资助项目(KQTD20180412181337494,JSGG20210802093207022,ZDSYS20201020162400001,GJHZ20200731095802007)。

摘　　要：分数阶Fourier变换作为传统Fourier变换的推广,与传统Fourier变换分析平稳信号类似,在实现对非平稳信号的时频分析过程中往往出现同样的频谱泄漏问题。为了提高分数阶Fourier变换与时频分析的精度,依据Kaiser窗可自由选择主瓣和旁瓣宽度的特性,提出一种基于Kaiser窗的分数阶Fourier变换算法,论述了Kaiser窗在分数阶Fourier变换中的作用原理,从理论上推导出一般信号基于Kaiser窗的分数阶Fourier变换解析时频表达式以及特性,最终得到非平稳信号的时频分布与时变结构参数识别算法。通过任意线性调频信号的仿真算例以及非平稳激励三层框架结构振动台试验,对结构进行瞬时频率识别和算法的验证。结果表明,瞬时频率识别值与理论值和试验结果吻合良好,Kaiser窗可以提高分数阶Fourier变换算法时频分析的精度,体现出该方法有一定的鲁棒性。As a generalization form of traditional Fourier transform to deal with non-stationary signals,the fractional Fourier transform often faces the same spectrum leakage problem as the traditional Fourier transform in analyzing stationary signals.In order to reduce the spectrum leakage error and improve the accuracy of fractional Fourier transform and time-frequency analysis,according to the characteristic that the Kaiser window can freely choose the width of main lobe and side lobe,this paper proposes an algorithm of fractional Fourier transform combined with Kaiser window.The function principle of Kaiser window in fractional Fourier transform is discussed.The theoretical formula of time-frequency representation for Kaiser window based fractional Fourier transform is then derived.The time-frequency distribution and time-varying structure parameter identification algorithm of non-stationary signals are obtained.The feasibility of the proposed method is verified by a simulated linear frequency modulation signal and a three-storey model frame excited by non-stationary inputs through a shake table in the laboratory.It is demonstrated that the identified instantaneous frequencies of the proposed method are in good agreement with the theoretical values and involved Kaiser window in fractional Fourier transform does increase the accuracy to identify the time-varying parameters with a certain robustness.

关 键 词：时变结构 分数阶FOURIER变换 频谱泄漏 KAISER窗 时频分布 

分 类 号：TU311.3[建筑科学—结构工程] TN911.6[电子电信—通信与信息系统]