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In this paper, we propose a simple frequency-domain interpolation technique for the discrete Fourier transform (DFT). This interpolation technique can significantly improve the frequency and phase resolution capabilities of the DFT without increasing the size of the DFT (the number of points used for the DFT). This new technique employs a dividing point in the amplitude and phase spectra. Suitable areas of application include joint estimation of fine frequency and phase offsets in burst-mode digital transmission.