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，the existing time-shift phase difference correction method cannot eliminate phase ambiguity in all cases but only at particular time-shift positions，which degrades the accuracy．In light of this，the analysis and the improvement of phase difference cor-rection method was discussed in this paper．A phase difference correction method based on wrapping was proposed to eliminate phase ambiguity when the time shifting digit L is not more than the effective point number N．In addition，one-point and N-point time shifting methods were discussed to omit phase wrapping．The results of nu-merical simulation show that the improvement reaches greater stability and the two methods can achieve a frequency precision of 10-7 order of magnitudes