Fast statistically efficient algorithms for single frequency estimation

In this article three new estimators of the frequency of a single complex sinusoid are presented. The "rotate-add-decimate" (RAD) method of Crozier is first modified to more closely approach the Cramer-Rao bound, with the same computation. A second estimator almost achieves the CRB above an SNR threshold approximately 1dB above that of RAD. It can be shown to achieve the CRB for high SNR using log₂N arctangents and 2N MAC. A third method matches the SNR threshold of RAD and achieves the CRB at high SNR with log₂N arctangents and 3N MAC.