Abstract: The amplitude spectrum properties of symetric windows were explored.First, the spectrum peak at ω=0 is the maximum point, according to this item,the parameter of single frequency signal can be unbiasedly estimated out by searching the signal amplitude spectrum maximum.Second,the main lobe width is greater than 4π/T,hence there are at least 2 FFT spectrum lines in main lobe,and the amplitude of 2 lines nearest to ω=0 get maximum and second maximum, which can be used to determine the searching scope. Third,all the spectrums of the window in finite time domain were damped oscillating,which means that it is imposible to　eliminate side lobes completely.