A New Gradient-Based Adaptive Algorithm Estimating Sinusoidal Signals in Arbitrary Additive Noise

摘要

In this paper, a new gradient-based adaptive al- gorithm for the estimation of discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is proposed based on a summed least mean squared error criterion. This algorithm requires exactly the same number of multiplications as the conventional LMS al- gorithm, and presents much improved performance in both white and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm in colored additive noise, and point out when its performance deteriorates. Then, a summed least mean squared error criterion is proposed, which leads to the above-mentioned new gradient-based adaptive algorithm. The performance of the proposed algorithm is also analyzed for a sin- gle frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.