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An Analytical Solution to Jacobsen Estimator for Windowed Signals

Interpolated discrete Fourier transform (DFT) is a well-known method for frequency estimation of complex sinusoids. For signals without windowing (or with rectangular-windowing), this has been well investigated and a large number of estimators have been developed. However, very few algorithms have been developed for windowed signals so far. In this paper, we extend the well-known Jacobsen estimator to windowed signals. The extension is deduced from the fact that an arbitrary cosine-sum window functions are composed of complex sinusoids. Consequently, the Jacobsen estimator for windowed signals can be formulated as an algebraic equation with no approximation and thus an analytical solution to the estimator can be obtained. Simulation results show that our approach improves the performance in comparison with the conventional interpolated DFT algorithms for windowed signals.