Statistical description of the sine-wave frequency estimator provided by the interpolated DFT method

This paper describes the effect of the spectral interference and wideband noise on the accuracy of the sine-wave frequency estimator provided by the Interpolated Discrete Fourier Transform (IpDFT) method based on some commonly used cosine windows. It is shown that the spectral interference contribution from the image component has a sinusoidal behaviour with respect to the sine-wave phase and the expression for its amplitude is derived. Also, a simple expression for the variance of noise contribution is derived. Based on the achieved results, the Probability Density Function (PDF) of the sine-wave frequency estimator is obtained. The accuracy of each expression derived in the paper is verified by means of computer simulations. Furthermore, the accuracy of the PDF of the sine-wave frequency estimator is verified by means of experimental results.

► We describe the statistical behavior of the sine-wave frequency estimator provided by the IpDFT method.
► The spectral interference exhibits a sinusoidal behavior with respect to the sine-wave phase.
► The wideband noise contribution is normally distributed.
► We derive the analytical expression of the PDF of the sine-wave frequency estimator.
► The accuracies of the derived expressions are confirmed through both computer simulations and experimental results.