A comparative study of interpolation discrete fourier transform algorithms under strong noise

Abstract

It is a pervasive problem to accurately estimate the frequency of sinusoids contaminated by random noise, which has existed in many signal processing areas, including the application in mechanical fault diagnosis and prognostics. The interpolation discrete Fourier transform (DFT) method, employed in frequency domain, is one of the most well studied frequency estimation methods. In this paper, a comparison has been made on the noise performance of various frequency estimators based on interpolation DFT algorithm with rectangular window or the Hanning window. The probability distribution of estimation errors returned by different frequency estimators as a function of frequency deviation, rather than the root mean square error of estimates which is usually adopted in the past references, is considered. The study presents a more thorough understanding of the advantages and deficiencies of the current interpolation DFT algorithms, which may provide a reference for researchers in selecting a proper algorithm so as to meet the specific requirements.