Accurate normalized frequency estimation by the three-point interpolated DFT method with rectangular window

This paper focuses on the estimation of a sine-wave normalized frequency by the three-point interpolated discrete Fourier transform (IpDFT) method with rectangular window. A constraint on the integer number of recorded sine-wave cycles is derived to ensure that the spectral interferences from the image components of the spectrum on the normalized frequency estimation are practically neglected. The statistically efficiency of this method, which applies to a sine-wave corrupted by a stationary white noise is investigated with respect to the unbiased Cramer-Rao (CR) lower bound. Moreover, a constraint on the number of acquired samples which ensures accurate estimates with a high confidence level is derived. The derived expressions are validated by means of computer simulations.