Abstract
It is well known that frequency estimation exhibits a threshold effect: as the SNR dips below a certain value (while the number of data points remains fixed) the estimate's variance increases rapidly, and the Cramer-Rao bound is no longer attainable. A simple, explicit formula for this threshold is derived for the case of a single complex sinusoid in white Gaussian noise. Since the presence of multiple frequencies raises this threshold, the formula serves as a lower bound for more complex problems. Because of the duality between time series and sensor arrays, the threshold is also applicable to angle of arrival estimation of a plane wave.
Cite
CITATION STYLE
Steinhardt, A. O., & Bretherton, C. (1985). THRESHOLDS IN FREQUENCY ESTIMATION. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings (pp. 1273–1276). IEEE. https://doi.org/10.1109/icassp.1985.1168170
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