Uncertainty analysis of the normalized frequency estimation by Multipoint Interpolated DFT Approach

In this paper the influence of a stationary white noise on the estimation of a sine-wave normalized frequency by using a Weighted Multipoint Interpolated Discrete Fourier transform (WMIpDFT) method is investigated. The expression of the normalized frequency estimates uncertainty is derived in the case when a H-term maximum sidelobe decay window (H ges 2) is used and the number of interpolation points is 2J + 1 (J ges 1). Based on this expression the statistical efficiency of the WMIpDFT method with respect to the unbiased Cramer-Rao lower bound is investigated. Moreover, a constraint on the minimum number of acquired samples which ensures accurate estimates of the normalized frequency with a high confidence level is derived. All the derived expressions are validated by means of computer simulations.