全相位FFT相位差频谱校正法改进

摘要

The phase difference correcting spectrum method based on all-phase fast Fourier transform (FFT) calculates the conventional FFT without effects of negative frequency. As a result, there is a decline in accuracy of low-frequency signal parameters estimation. Aiming at this problem, an improved phase difference correcting spectrum method based on all-phase FFT is proposed. The effects of negative frequency to FFT are considered in classic FFT. The all-phase FFT spectrum analysis theory and the phase difference correcting method are introduced. The cause that the negative frequency has a negative impact on low-frequency signal spectrum analysis is analyzed. The equations of frequency, amplitude and phase estimating for single-frequency signals sampled in non-integer-period are derived with the effects of negative frequency to spectrum analysis be-ing considered. The simulation results show that the improvement of considering negative frequency contribu-tion is able to improve the accuracy in low-frequency cosine signal parameter estimation in the conventional way, and the anti-noise ability of the original algorithm is also improved.%基于全相位快速傅里叶变换(fast Fourier transform,FFT)的相位差频谱校正法由于未计及负频率的影响,导致低频信号参数估计精度下降.针对此问题,提出一种改进的全相位FFT相位差频谱校正法,该算法在计算传统FFT时,消除了负频率对频谱分析的影响.介绍了全相位频谱分析原理及全相位FFT相位差频谱校正算法,分析了负频率对低频信号频谱分析造成影响的原因.在计及负频率影响的情况下推导了非整周期采样条件下单频余弦信号的频率、幅值和相位的计算公式.仿真结果表明,计及负频率影响的算法提高了基于全相位FFT的相位差频谱校正法对低频余弦信号参数估计的精度,算法抗噪性能得到改善.