Adaptive algorithm based on least mean p-power error criterion for Fourier analysis in additive noise

This abstract presents a novel adaptive algorithm for the estimation of discrete Fourier coefficients (DFC) of sinusoidal and/or quasiperiodic signals in additive noise. The algorithm is derived using a least mean p-power error criterion. It reduces to the conventional LMS algorithm when p takes on 2. It is revealed by both analytical results and extensive simulations that the new algorithm for p=3, 4 generates much improved DFC estimates in moderate and high SNR environments compared with the LMS algorithm, whereas both have similar degrees of complexity. Assuming the Gaussian property of the estimation error, the proposed algorithm, including the LMS algorithm, is analyzed in detail. Elegant dynamic equations and closed-form noise misadjustment expressions are derived and clarified.