Fast algorithms for single frequency estimation

In this paper, some new estimators of the frequency of a single complex sinusoid are presented. The rotate-add-decimate (RAD) method of Crozier is first refined to more closely approach the Cramer-Rao Bound (CRB). An additional modification yields an unbiased estimator (ERAD) that essentially achieves the CRB above a signal-to-noise ratio (SNR) threshold comparable to that of RAD. In addition, this estimator is proven to achieve the CRB for high SNR. The ERAD method requires approximately 2N complex multiply-adds and log₂N arctangents. A modified ERAD (MERAD) is proposed that matches the SNR threshold and computational complexity of the RAD method (approximately 3N complex multiply-adds and log₂N arctangents) but achieves the CRB for high SNR.