A new gradient-based adaptive algorithm estimating sinusoidal signals in arbitrary additive noise

In this paper, a new gradient-based adaptive algorithm for the estimation o f discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is propo sed based on a summed least mean squared error criterion. This algorithm re quires exactly the same number of multiplications as the conventional LMS a lgorithm, and presents much improved performance in both whits and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm i n 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 performan ce of the proposed algorithm is also analyzed for a single frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.