Analysis of the bias affecting the interpolated DFT frequency estimator

In this paper, an analytical expression for the overall bias of the complex-valued noisy sine wave frequency estimator returned by the interpolated discrete Fourier transform algorithm is derived. That bias is due to the effect of both the algorithm intrinsic approximation when rectangular windowing is adopted and wideband noise. The effect of the number of analyzed samples and the signal-to-noise ratio on the ratio between the overall estimation bias and the estimator standard deviation is also investigated. In addition, leveraging on the derived expression, a frequency estimator that compensates for the contribution due to the algorithm intrinsic approximation is proposed and its accuracy is compared with that of the classical frequency estimator.