The origin of initial-phase sensitivity and the main factors influencing the level of initial-phase sensitivity are analyzed

then the method of reducing initial-phase sensitivity is proposed to increase the stability of the windowed discrete Fourier transform (DFT) algorithm. Theoretical analysis and numerical results indicate that randomness of initial-phase will bring about harmonic amplitude calculation errors. However

not every windowed DFT algorithm needs consideration of the initial-phase sensitivity. Under a definite frequency deviation

the level of initial-phase sensitivity is determined by the sidelobe peak level of window functions. The lower the sidelobe peak level is

the smaller the initial-phase sensitivity will be. The sidelobe peak level -58 dB can be a reference to determining whether the initial-phase sensitivity needs to be considered in the window functions. In practical engineering

the method of increasing the length of time record can be used to reduce the influence of initial-phase sensitivity.