Frequency estimators with high resistance to interference from image frequency components

Abstract

This paper presents an improved frequency estimation algorithm based on the interpolated discrete Fourier transform. High-accurate frequency estimation can be achieved by taking the geometric mean of two independent estimates, which are derived from the real parts of the two largest spectral bins and the imaginary parts, respectively. In situations where only a small number of sine wave cycles are observed, the ability of the algorithm to cancel interference from image frequency components results in improvements in accuracy. The residual errors of the proposed algorithm have been theoretically analyzed with maximum side-lobe decaying windows, since the windows have simple and uniform analytical expression of interpolation algorithm. The performance of the proposed algorithm was investigated using both Hanning and three-term maximum side-lobe decaying windows. A comparative analysis of systematic errors and noise sensitivity was performed between the new algorithm and traditional algorithms. Both the root mean squared error and the probability density of the errors were investigated under noisy conditions. Simulation results demonstrated that the new algorithm is not only highly resistant to interference from image components but is also resistant to the effects of random noise. The results presented in the paper are useful for identifying the best choice of algorithm in practical engineering applications.