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An algorithm for instantaneous estimation of sinusoidal signals basing on numerical differentiation is presented in this paper. With all parameters unknown, the signal is sampled at a fixed frequency, and central Lagrange interpolation of multi-points is employed for computation. The proposed algorithm is adaptive to any sinusoidal signal with its frequency varying from 1 Hz to 4 kHz, its amplitude varying from 0.1 V to 100 V, and its phase varying from 0 to 360. The proposed algorithm for frequency estimation needs in most 1 cycle, with an accuracy of more than 0.001%. An example for test study is simulated in Matlab software with satisfactory results.