全相位FFT时移相位差频谱校正分析及改进

Analysis and Improvement of Time-Shift Phase Difference Spectral Correction Based on All-Phase FFT

全相位快速傅里叶变换(apFFT)拥有良好的频谱泄漏抑制能力.然而,现有全相位时移相位差校正方法只能在特殊时移位发挥效果,未能完全消除相位测量中的相位模糊,在部分情形下校正结果会出现较大偏差.针对该缺陷,对全相位相位差校正进行理论分析,提出了利用相位压缩运算在时移位数L不大于有效数据点数N时消除相位模糊的一般性校正方法,并对能省略相位压缩运算的时移1位和N位两种特殊情形进行分析.数值仿真结果表明,改进后方法的稳定性明显优于改进前,无噪时时移N位和时移1位的频率校正误差可到10^(-7)数量级.

All phase fast Fourier transform(apFFT)has eminent ability to restrain spectral leakage.However,theexisting time-shift phase difference correction method cannot eliminate phase ambiguity in all cases but only at particulartime-shift positions,which degrades the accuracy.In light of this,the analysis and the improvement of phasedifference correction method was discussed in this paper.A phase difference correction method based on wrappingwas proposed to eliminate phase ambiguity when the time shifting digit L is not more than the effective point numberN.In addition,one-point and N-point time shifting methods were discussed to omit phase wrapping.The results ofnumerical simulation show that the improvement reaches greater stability and the two methods can achieve a frequencyprecision of 10-7 order of magnitudes.