Signal Processing
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Research Letters in Signal Processing
Optimal filters for extraction and separation of periodic sources
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Optimal filter designs for separating and enhancing periodic signals
IEEE Transactions on Signal Processing
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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 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