Sine-wave parameter estimation by interpolated DFT method based on new cosine windows with high interference rejection capability

Abstract

The parameters of a sine-wave are often estimated by means of the classical Interpolated Discrete Fourier Transform (IpDFTc) method based on cosine windows since this method provides high accuracy while requiring low computational effort. When the number of acquired sine-wave cycles is small, estimation accuracy is heavily affected by the interference due to spectral leakage from both the sine-wave image component and other disturbance tones such as signal harmonics. To reduce both these detrimental effects new cosine windows are proposed in this paper. Their spectra exhibit a deep null close to the image component interfering frequency and the highest allowed sidelobe decay rate, so assuring minimization of long range spectral leakage. These windows are called Maximum Image interference Rejection windows with Rapid Sidelobe Decay rate (RSD) or simply, MIR-RSD windows. The analytical expressions of the sine-wave parameter estimators provided by the IpDFTc method based on the H-term MIR-RSD window (H≥2) are also derived. To assess the effectiveness of the MIR-RSD windows in rejecting the spectral interference when analyzing noisy or harmonically distorted sine-waves, the accuracy of the proposed frequency estimator is compared with those provided by other IpDFT frequency estimators through simulation and experimental results.