Estimates of frequencies of noise corrupted sinusoidal signals are often obtained from the zero locations of data adaptive or prediction error filters [1,2]. It is well known that the frequency estimation error decreases as the order of the prediction error filter is increased for a given data record length. In this paper, we explain this phenomenon, at high SNR by calculating the statistics of the estimation error.
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Tufts et al. (2005) studied this question.