A Fourier coefficient estimation method based on notch filters and an adaptive algorithm for sinusoidal signals in additive noise

Abstract

SUMMARYEstimating the amplitude and phase of a signal accurately even when the frequencies contained in the signal are already known is very important in many areas. The estimation accuracy and the estimation time are important issues in such areas and a method of improving both of these issues by combining the notch characteristics and the band passing characteristics of serially connected notch filters and an adaptive algorithm is presented in this paper. Computer simulations reveal that the performance of the proposed method is superior to previously proposed methods. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(2): 6573, 2002

Performance analysis of a Fourier coefficient estimation method using IIR‐BPFs and an LMS algorithm and improvement of its performance

“…Hence, in this case the convergence characteristics are identical to the normalized LMS algorithm. Also, the convergence speed of the mean square error of the estimated value does not depend on the power of the signal to be analyzed and hence is known to be regulated only by µ [8]. As a result, the improved method in which the power of the analyzed signal is decreased by bandwidth division and the BPLMS method are compared for identical µ.…”

“…Note that A i and B i are given by Eqs. (8) and (9). Equation (7) is obtained by solving the recursive equation for the mean square error of the estimate in the time domain:…”

“…To date, signals with nonharmonic relation in which white noise and interference exist singly or together have been studied [8][9][10]. All of them are combinations of FIRor IIR-type filters having bandpass characteristics with the LMS algorithm.…”

Improvement of a Fourier coefficient estimation method using an adaptive algorithm and its performance analysis

“…The steady-state mean square error ε ∞ of the estimate, the convergence condition of the square error for µ, and the convergence time constant τ are found by using Eqs. (6), (7), and (8), respectively [10,12]. Here E[⋅] stands for the expectation value operation.…”

“…The authors have used combinations of the LMS algorithm with FIR and IIR bandpass filters to improve the Fourier coefficient estimation of nonharmonic signals involving disturbances such as white noise, interference, or both [12][13][14][15]. As regards adaptive algorithms, it is important to improve accuracy while preventing an increase in computational complexity.…”