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The theoretical basis for the development of a power-spectrum centroid detector is presented, and known and new applications to centroid detection are described. Based on these applications, the requirements are formulated for a versatile centroid detector which can be employed in various types of ultrasonic doppler systems. An analysis method for centroid estimation is developed and applied to the correlation- and √f-type detectors. Closed-form expressions for estimation errors are derived and used for detector evaluation with and without additive noise at the input. A noise-reduction technique is introduced that enables accurate centroid detection despite the presence of strong input noise. Based on the results of this analysis, theoretical comparisons of the detectors, and system requirements, the √f detector is selected for implementation and use.
Gerzberg et al. (Tue,) studied this question.