Standardized sine-wave fitting algorithms, extensions and applications

The objective of this paper is to present the statistical properties of the IEEE-STD-1057/IEEE-STD-1241 sine-wave fitting algorithms. The proper Cramer-Rao bound is derived for both the three-parameter and four-parameter algorithms. Further, we investigate the residual, and derive its statistical properties, in both the three- and four-parameter fitting case. In a practical setup were the frequency is almost known, we derive an analytical expression for the mean of the residual. By analysis we compare the two methods and state in which case one should use one over the other. Finally, we present some numerical evaluations confirming our analytical findings.

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