基于DFT相位的正弦信号幅度高精度估计

High accuracy amplitude estimation of sinusoid based on the phase of DFT

针对利用 DFT幅度估计正弦信号幅度因频谱泄漏引起较大误差的问题 ,首先根据 DFT最大谱线的幅度对信号幅度进行粗略估计 ,然后将采样信号分两段再做 DFT,由两个 DFT在最大谱线处的相位得到信号的初始相位 0 的估计值 ,根据 0 估计信号频率与 DFT最大谱线对应的频率的偏差 δ,利用 δ对幅度的粗略估计进行修正 ,得到信号幅度的高精度估计 .Monte Carlo模拟结果表明幅度估计精度大大提高 ,估计方差接近 Cramer Rao下限 .

Due to the spectral leakage, amplitude estimation of sinusoid based on DFT bears significant errors. A high accuracy amplitude estimation method of sinusoid based on the phase of DFT is presented in this paper. The coarse estimation of the amplitude is made with the amplitude of the maximum spectral line of DFT first, then the sampled data are divided into two segments and DFT is applied on each segment separately. The initial phase of the sinusoid, φ 0 , is estimated from the phases of the two DFTs. Then the deviation of the frequency of the sinusoid from the frequency corresponding to the maximum spectral line of the DFT, denoted as δ , is estimated according to φ 0 . Finally, the coarse amplitude estimation is compensated according to the estimation of δ . Monte Carlo simulation results show that the amplitude estimation of the sinusoid is greatly improved and the variance of amplitude estimation is close to the Cramer Rao bound.