On the Estimation of the Parameters of a Real Sinusoid in Noise

We propose and comprehensively analyze a computationally efficient algorithm to estimate the parameters of a real sinusoidal signal in noise. This method uses the fast Fourier Transform and is, therefore, computationally efficient. Accounting for the interference due to the negative spectral component allows the frequency to be estimated very accurately. Estimates of the amplitude and phase are derived in the process and are necessary for the suppression of the leakage. Theoretical analysis establishes that the estimator is asymptotically unbiased and achieves the Cramér-Rao lower bound. Simulation results are presented to verify the theory and demonstrate that the estimation performance is superior to other estimators in the literature.