Amplitude estimation of sinusoidal signals: Survey, new results, and an application

Petre Stoica, Hongbin Li, Jian Li

Research output: Contribution to journalArticlepeer-review

142 Scopus citations

Abstract

This paper considers the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise. A relatively large number of amplitude estimators, which encompass least squares (LS) and weighted least squares (WLS) methods, are described. Additionally, filterbank approaches, which are widely used for spectral analysis, are extended to amplitude estimation. More exactly, we consider the recently introduced matched-filterbank (MAFI) approach and show that by appropriately designing the prefilters, the MAFI approach to amplitude estimation includes the WLS approach. The amplitude estimation techniques discussed in this paper do not model the observation noise, and yet, they are all asymptotically statistically efficient. It is, however, their different finite-sample properties that are of particular interest to this study. Numerical examples are provided to illustrate the differences among the various amplitude estimators. Although amplitude estimation applications are numerous, we focus herein on the problem of system identification using sinusoidal probing signals for which we provide a computationally simple and statistically accurate solution.

Original languageEnglish
Pages (from-to)338-352
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume48
Issue number2
DOIs
StatePublished - 2000

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