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An algorithm for the estimation of the frequency of a complex sinusoid in noise is proposed. The estimator consists of multiple applications of lowpass filtering and decimation, frequency estimation by linear prediction, and digital heterodyning. The estimator has a significantly reduced threshold relative to existing phase-based algorithms and performance close to that of maximum likelihood estimation. In addition, the mean-squared error performance is within 0.7 dB of the Cramer-Rao bound (CRB) at signal-to-noise ratios (SNRs) above threshold. Unlike many autocorrelation and phase-based methods, the proposed algorithm's performance is uniform across a frequency range of -π to π. The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.