An Adaptive Estimation of Periodic Signals Using a Fourier Linear Combiner

Christopher Vaz, Xuan Kong, Nitish Thakor

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


Here, we present 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 included.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number1
StatePublished - Jan 1994

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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