全相位FFT相位测量法的抗噪性能

摘要

为研究全相位FFT(all-phase FFT,apFFT)测相方法的抗噪性能,本文不仅定性观察了不同信噪比(Signal to noise ratio,SNR)的噪声对apFFT的振幅谱图和相位谱图的影响,还定量分析了高斯噪声和量化噪声对测相性能的影响.并推导出apFFT测相方差的理论公式.仿真实验证明,apFFT测相方差与理论值吻合,远小于传统FFT测相方差,无需任何附加频率估计措施,其相位测量方差即可接近Cramer-Rao下限.%In order to study the anti-noise performance of the measuring phase method based on all-phase FFT (apFFT for short), the qualitative observation of the noisy effect on the apFFT amplitude and phase diagrams at different SNR levels is implemented, and the quantitative analysis of the performance of measuring method influenced by Gaussian noise and quantization noise is studied respectively. Then the theoretic variance formula of apFFT measuring method is deduced. Simulation verifies that the actual apFFT measuring phase variance is coincident with the theoretic value, and far lower than that of the conventional FFT. Moreover, the apFFT measuring phase variance approximates the Cramer-Rao lower bound without introducing any extra steps ofestimating frequency.