Dynamic phasor estimates through maximally flat differentiators

Estimates of the dynamic phasor and its derivatives are obtained using the weighted least-squares solution of a Taylor approximation with classical windows as weighting factors. It is demonstrated that the least-squares solution simultaneously approximates the time function and its spectrum, and this twofold solution in turn is equivalent to the simultaneous approximation of the ideal frequency responses of the differentiators at once on the bandpass centered at the desired central frequency. Therefore the differentiators are maximally flat in the interval centered at the desired frequency. The filters designed with the rectangular and Hamming windows are shown as examples of baseband differentiators.