【作者】 陈奎孚； 黄清； 张森文；

【Author】 Chen Kui Fu~1 Huang Qing~2 Zhang Sen Wen~2 (1.College of Sciences,China Agricultural University,Beijing,100083;2.Beijing Jiaotong University,Beijing,100044;3.The Institute of Applied Mechanics,Jinan University,Guangzhou 510632)

【机构】 中国农业大学理学院； 北京交通大学； 暨南大学应用力学研究所；

【摘要】 快速傅立叶变换(FFT)是估计周期成分的最重要方法,但是它对随机噪声的敏感性在振动领域很少受到关注,这是因为FFT的栅栏效应和谱泄漏引起的误差淹没了随机噪声的影响。目前发展的插值FFT完全克服了FFT的栅栏效应,为了进一步保证精度,必须研究插值FFT对随机噪声的敏感性。本文内容包括:1.研究正弦信号的Cramer-Rao界(CRB)的特性;对短数据,讨论了CRB如何随数据长度和初相位而变化。2.简要地回顾了插值FFT的发展历史。3.通过数值仿真比较了两个插值FFT(三谱线法和双谱线法)的统计特性。研究结果表明:1.最短采样长度应不低于0.825个信号周期;2.对长信号,两个插值FFT的性能相当;但对于短信号,双谱线法比较优越,它的方差与CRB吻合。更多还原

【Abstract】 The Fast Fourier Transform (FFT) is the most important techniques to estimate the parameters of a periodic component;however its sensitivity to random noise does not draw much attention in the vibration community.This fact is due to the error incurred by picket-fence effect of the FFT and the spectral leakage overrides the error caused by random noise.The currently developed interpolated FFT has eradicated the picket-fence effect off;consequently to ensure the FFT’s accuracy moreover,its sensitivity to noise was studied.Firstly,the Cramer-Rao bound (CRB) of a sinusoid was investigated numerically,especially the dependence of the CRB on the cycles in record and the initial phase for a short record.Secondly, the history of the interpolated FFT was reviewed briefly.Finally the statistics of two interpolated FFTs (double-line approach vs.triple-line approach) is compared.It is shown that,firstly,the recorded data covering at least 0.825 cycles is recommended. Secondly,for a long record,both approaches are comparable in performance,while the double-line approach is better than the triple-line approach for a short record.更多还原