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The coherent resampling (CR) algorithm, which improves the accuracy of discrete Fourier transform (DFT)-based power system frequency analysis, is described in the paper. The algorithm uses extended Kalman filter for instantaneous frequency tracking and fractional B-spline resampler for signal approximation. The CR algorithm is a software counterpart of synchronous sampling, i.e., sampling, synchronized with fundamental frequency of the signal. CR may either be applied to previously noncoherently sampled signals or to work in realtime. Frequency estimation, amplitude spectrum estimation and THD factor estimation results obtained by presented algorithm are compared to those obtained by other methods. Both simulated and real signals were used for tests. Brief summary of realtime DSP implementation of CR algorithm is also given.