基于加窗递推DFT算法的快速相位差校正法研究

Fast phase difference correction method by using recursive DFT with Blackman-harris window

计算谐波的相位差校正法利用间隔一个周期的两段连续N点时域采样信号并进行两次N点FFT变换,利用其对应离散谱线的相位差计算出频率变化量对幅值和相位进行校正。为了减少两次FFT运算量和提高实时性,采用了加余弦窗的递推DFT算法并利用间隔一个采样周期的两次DFT变换计算其对应离散谱线的相位差。由于加Blackman-harris窗函数的频谱泄漏影响小计算精度高,为了提高计算精度,采用加Blackman-harris窗截断,结合Blackman-harris窗的幅值修正系数公式可以准确校正幅值。为进一步提高计算速度,在计算幅值修正系数时还利用了嵌套形式的三次样条函数。通过仿真计算结果可以看出,频率误差小于0.000 1 Hz,幅值误差小于0.02%,相位误差小于0.5%,具有较高的精度。

A new method,phase difference correction metho d,is presented to correct the frequency and phase by separating the continuous time-domain signal into two segments and making FFT respectively,then correct the phase difference of corresponding discrete spectral lines.For minimizing the enormous computational complexity of FFT,the method us es recursive DFT,which makes the computation more simplified.The Blackman-harris window has small influence of frequency spectrum leakage,and the results of computation are consicer than before.So Blackman-harris window is adopted.The amplitude can be rectified using the formula of window function,and spectral analysis is also used for improving the calculatio n precision.The results show that the frequency error is less than 0.0001 Hz,amplitude error less than 0.02%,and phase error less than 0.5%..