基于DFT的正弦波初相估计算法及误差分析

Phase estimation of sinusoid signal based on DFT and error analysis

提出一种基于DFT(Discrete Fourier Transforms)频谱相位信息的正弦波初相高精度估计方法.该方法通过截取正弦波的两段长度不同的离散序列,利用它们的DFT系数来消去正弦信号的频率项,从而估计其初相.同时,给出了在高斯白噪声背景下,利用该种方法进行正弦波初相估计的均方根误差计算公式,此公式表明了均方根误差与信噪比及FFT(FastFourier Transforms)长度之间的关系.并以此均方根误差最小化为目标,对该估计方法进行了优化改进,得到方法中参数的最优选取方案.选择最优参数的过程即是对以均方根误差最小为目标的整数规划问题的求解过程.应用Monte Carlo仿真,将改进后的算法的性能与已有的几种典型算法的性能及Cramer-Rao下限进行了分析比较,并验证了所推导的均方根误差计算公式的正确性.

A fast and accurate estimation technique of initial phase of single-tone signal based on the phase of discrete Fourier transforms （DFT） spectrum was proposed. The initial phase is obtained by removing the frequency item in the muhinomial using the DFT coefficient which is from two discrete sinusoid signal sequences of different length. The root mean square error （RMSE） formula of initial phase estimation under Gaussian white noise was derived that presents the relationship among RMSE, fast Fourier transforms （FFT） length and signal noise ratio （SNR）. The parameters in the formula were studied and optimized to minimize the RMSE. The process of which is to solve the integer programming problem with the objective function that RMSE is minimal. Through Monte Carlo simulation, the performance of the improved technique was compared with other typical algorithms and Cramer-Rao lower bound （CRLB） , the RMSE formula is found to be effective.