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Description
Accurate frequency estimation is central to turn-by-turn (TbT) data analysis. This task is of intrinsic interest and enables the subsequent recovery of the amplitudes and phases of the component of the harmonic. In TbT data from numerical simulations, several algorithms exhibit better convergence with respect to FFT frequency estimation, improving the scaling of the frequency error from $\mathcal{O}(1/N)$ to $\mathcal{O}(1/N^p)$ for $p > 1$ by exploiting the quasiperiodic structure of the signals. However, in TbT data from experimental measurements, measurement noise partially breaks the quasi-periodicity and degrades the scaling of the frequency error. We investigate the accuracy and spread of frequency error estimates for a noisy harmonic signal using several methods, with and without spectral windowing. We explore bias-variance trade-offs coming from windowing and compare observed dispersion with the Cramér-Rao lower bound.
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