Improvement of a Fourier Coefficient Estimation Method Using an AdaptiveAlgorithm and its Performance Analysis

There are many applications where it is necessary to estimate accurately the amplitude and phase of signals when the information regarding the frequencies is obtained in advance. This paper presents a new algorithm for estimating more accurately Fourier coefficients of a signal contaminated by additive noise where sinusoidal frequencies of interest are not distributed uniformly. In the proposed method, Fourier coefficients are adaptive parameters. It uses averaged gradient signals and has almost the same acquisition time as the conventional LMS algorithm with more accurate estimation. The performance analysis of the proposed method is presented and its validity and limits are verified under various conditions by computer simulations. Furthermore, it is shown that the proposed method has especially better performance compared with the LMS algorithm in case that both of the number of frequencies and the step size parameter, μ, are large.