Accuracy of Sine Wave Frequency Estimation by Multipoint Interpolated DFT Approach

This paper focuses on the frequency-domain estimation of the normalized frequency of a sine wave corrupted by a stationary white noise. The weighted multipoint interpolated discrete Fourier transform method is considered, and its effect on both the spectral interference due to the image component and the additive wideband noise is taken into account. In particular, the expression of the combined standard uncertainty of the estimator is derived in the case when the H-term maximum sidelobe decay window (H ≥ 2) is used, and the number of interpolation points is 2J + 1 (J ≥ 1). Based on this expression, the number of interpolation points that minimize the estimator-combined uncertainty can be determined. The derived results are validated by means of computer simulations and applied to experimental data.