Analysis of the influence of observation starting time on FFT-based phase estimation of sinusoid

The initial phase estimation technique based on FFT of single-tone signal is reviewed first. By employing the same signal expression as used in all-phase FFT, estimation equation of the middle-point phase of the signal is derived. It is proved that middle-point phase estimation of conventional FFT has the same property as all-phase FFT, i.e., the estimation is not affected by the deviation between the frequency of the sinusoid signal and the frequency the maximum spectral line of the FFT stands for. This property leads to the avoidance of the correction to the phase estimation. The formula for evaluating the variance of the estimation is also derived. Finally computer simulation results are given.