An adaptive estimation of periodic signals using a Fourier linear combiner
- 1 January 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 42 (1) , 1-10
- https://doi.org/10.1109/78.258116
Abstract
Presents an adaptive algorithm for estimating from noisy observations, periodic signals of known period subject to transient disturbances. The estimator is based on the LMS algorithm and works by tracking the Fourier coefficients of the data. The estimator is analyzed for convergence, noise misadjustment and lag misadjustment for signals with both time invariant and time variant parameters. The analysis is greatly facilitated by a change of variable that results in a time invariant difference equation. At sufficiently small values of the LMS step size, the system is shown to exhibit decoupling with each Fourier component converging independently and uniformly. Detection of rapid transients in data with low signal to noise ratio can be improved by using larger step sizes for more prominent components of the estimated signal. An application of the Fourier estimator to estimation of brain evoked responses is includedKeywords
This publication has 13 references indexed in Scilit:
- Adaptive Fourier estimation of time-varying evoked potentialsIEEE Transactions on Biomedical Engineering, 1989
- Fundamental relations between the LMS algorithm and the DFTIEEE Transactions on Circuits and Systems, 1987
- On almost sure convergence of adaptive algorithmsIEEE Transactions on Automatic Control, 1986
- A variable step (VS) adaptive filter algorithmIEEE Transactions on Acoustics, Speech, and Signal Processing, 1986
- Convergence analysis of LMS filters with uncorrelated Gaussian dataIEEE Transactions on Acoustics, Speech, and Signal Processing, 1985
- Second-order convergence analysis of stochastic adaptive linear filteringIEEE Transactions on Automatic Control, 1983
- Convergence in distribution of LMS-type adaptive parameter estimatesIEEE Transactions on Automatic Control, 1983
- Stationary and nonstationary learning characteristics of the LMS adaptive filterProceedings of the IEEE, 1976
- The complex LMS algorithmProceedings of the IEEE, 1975
- Adaptive noise cancelling: Principles and applicationsProceedings of the IEEE, 1975