Frequency estimation of the non-stationary signals using interpolated DFT

The measurement of a periodic signal with an unknown changing frequency can be well done with an interpolation of DFT (discrete Fourier transformation). This paper presents first an analysis of errors of the DFT coefficients caused by frequency variation. The relations between the stationary case errors and the non-stationary ones are carried out. The bias removal of the interpolation algorithms are studied for rectangular and Hanning windows. Finally, a new interpolation technique that allows very accurate measurements of the instantaneous frequency is proposed Interpolations with longer time of measurement and with larger number of points decrease the systematic errors. The proposed algorithm presents: very fast recovery time (3/4 of a new period), robustness to the amplitude variation, and very high accuracy (the maximal relative error is under one thousandth at slower frequency changes).