短记录加汉宁窗的频谱校正

SPECTRUM CORRECTION FOR SHORT RECORDS WEIGHTED BY A HANNING WINDOW

基于解析单频模型建立的频谱校正方法难以应用于短记录的频谱校正,因为这时正频率附近的频谱显著偏离解析单频模型,背后的原因是实数信号中负频率分量的泄漏干扰。针对短记录加汉宁窗,给出了一种显式频谱校正方法,它利用局部谱峰附近的三条谱线。采用仿真手段对提出的方法进行了考核。不同仿真样本所含的信号周期数(CiR)从0.05变化到5,步长为0.01;相位从0°变化到179°,步长为1°。结果表明:1)当CiR>1时,最大频率误差小于10-10Δω(Δω是快速傅里叶变换的频率分辨率),而幅值相对误差和相位误差的上限分别不超过10-10和10-7度;2)当CiR<1时,误差总体趋势随频率下降而增加,但即使对CiR=0.05,频率误差也不超过4×10-8Δω;3)精度最高的条件仍然是整周期采样。

Spectrum correction approaches based on the model of an analytical signle tone can hardly be applicable to short records.It owes to significant influence from negative frequency components in a real signal.An explicit specturum correction approach is proposed to short records weighted by a Hanning window.This approach makes use of three specturum lines around the main lobe.The proposed approach is validated by simulation.The parameters in the simulated samples have a widespread distribution.The oscillation cycles in record(CiR) in these samples vary from 0.05 to 5 by step 0.01,and each CiR includes samples with initial phase increasing from 0°to 179°by step 1°.The maximum error with the proposed approach among 180 phase samples per CiR is inspected.The simulation results show that,firstly,for CiR >1,the frequency error of the proposed approach is no greater than 10-10 Δω where Δω is the frequency resolution of the canonical fast Fourier transformation,the relative amplitude error and phase error are no greater than 10-10and(10-7)°,respectively;secondly,for CiR < 1,all above three errors increase as CiR decreases,however,even for CiR=0.05,the three errors are less than 4×10-8Δω,10-6and(10-4)°,respectively;thirdly,the local minimum error aligns with coherent sampling by an integer GiR.