According to the special requirements of the ground fault test signal of the primary and secondary fusion switch

an improved three-point interpolated DFT algorithm to achieve high precision frequency estimation is proposed under the very small cycles in this paper. Based on the maximum sidelobe decay window（MSDW）

the algorithm splits the real and imaginary parts of the DFT spectrum and calculates the three-point interpolation separately.Then the geometric mean calculation is used to eliminate the negative frequency leakage interference. Finally

according to the obtained interpolation formula

the statistical characteristics of the algorithm under noise are strictly mathematical proof. Furthermore

multiple simulations are used to verify the validity and accuracy of the algorithm.The results show that the algorithm can not only maintain relatively stable and high accuracy of correction and estimation under any fluctuation period

but also has strong resistance. Finally

it is applied to the frequency estimation of the measured ground fault waveform signals

which lays the foundation for the accurate reproduction of the input and output ground fault waveform of the 12 kV primary and secondary fusion detection device.