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This paper focuses on the amplitude estimation by a multipoint interpolated discrete Fourier transform (DFT) method. Accurate results are obtained using the weighted multipoint interpolated DFT (WMIpDFT) method with maximum sidelobe decay windows. In addition, using the WMIpDFT method with maximum sidelobe decay windows, it is mathematically proven that the systematic errors affecting the amplitude estimation decrease as the number of interpolation points and/or the window order increases. Computer simulations confirm the accuracy of the derived expressions. Moreover, the influence of white Gaussian noise on the amplitude estimations has been analyzed by means of computer simulations.