A novel method for fundamental frequency measurement of multi-harmonic signals with noises using numerical differentiation

A high-accuracy, wide-range frequency estimation algorithm for the non-sinusoidal signals with white Gaussian noises basing on a numerical differentiation and central Lagrange interpolation is proposed in this paper. The proposed algorithm needs 7 sample points for frequency estimation of the signals with 3 order harmonics. The sample frequency is not restricted by the real value of the frequency of the non-sinusoidal signal and the mean of the noises. Under conditions with white noise, the frequency of the signal is estimated at an error of 0.001% over 1 Hz to 1000 kHz with the amplitudes of 1st, 2nd and 3rd of the non-sinusoidal signal varying from 1 to 320 V and the phase angle of 1st, 2nd and 3rd of the non-sinusoidal signal varying from 0 to 360 in at most half cycle. Using Matlab software, the simulation results of the test example are satisfactory.