Analytical solution of DFT interpolated frequency estimator for Hanning windowed signal

Abstract

Frequency estimation from discrete Fourier transform (DFT) coefficients of a rectangular windowed signal under the influence of additive white noise is a well studied problem in signal processing. In its simplest form, the process involves finding the spectral peaks. When higher frequency resolution is required, a frequency offset can be found from the interpolation of DFT coefficients. However, most of the past researches focus on monotonic cisoid signals. In practical situations where multiple harmonics are present, the sidelobes from other harmonics interfere with the estimation of the harmonic being considered. In this case, windows with smaller sidelobes such as Hanning window are preferred over rectangular window. Given the increased mathematical complexity of Hanning window, analytical solution has not yet been available for DFT interpolation. In this paper, we derive an exact analytical solution of the estimated frequency from DFT interpolation of Hanning windowed signal. In experiments, we show that the new analytical solution is accurate for monotonic cisoid signal and can considerably reduce the effect of interharmonic interference as compared to previous rectangular windowed methods.