Abstract
In this paper, the problem of estimating the discrete Fourier coefficients of sinusoidal signals with known arbitrary frequencies in additive noise using a least mean square (LMS) adaptive algorithm is treated in some detail. Frequency response analysis reveals that the LMS algorithm proposed for a single-frequency case possesses the characteristics of an IIR notch filter. The estimator is analyzed for its convergence and mean square error (MSE) due to the additive noise and the mismatch between the signal and the designated frequencies. Difference equations governing the dynamic behavior of the estimator are also derived. The analyses of a single-frequency case are extended to a multifrequency case. Simulations are performed to confirm the theoretical results.
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