Publication:
Nonmatrix cramer-rao bound expressions for high-resolution frequency estimators

dc.contributor.buuauthorDilaveroğlu, Erdoğan
dc.contributor.departmentMühendislik Fakültesi
dc.contributor.departmentElektronik Mühendisliği Bölümü
dc.date.accessioned2021-06-29T10:15:20Z
dc.date.available2021-06-29T10:15:20Z
dc.date.issued1998
dc.description.abstractAnalytical expressions are derived for the Cramer-Rao (CR) lower bound on the variance of frequency estimates for the two-signal time-series data models consisting of either one real sinusoid or two complex sinusoids in white Gaussian noise. The expressions give the bound in terms of the signal-to-noise ratio (SNR), the number N of data samples, and a function dependent on the frequency separation and the initial phase difference between the two signal components of each model. The bounds are examined as the phase difference is varied, and the largest and smallest bound expressions and the corresponding critical values of the phase difference are obtained, The exact expressions are analyzed for the case of small frequency separations delta w It is found that the largest bound is proportional to ( N . delta w )(-4)/N-3. SNR and that the smallest bound is proportional to ( N .delta w )(-2)/N-3 SNR for small delta w. Examples indicate that the small delta w results closely approximate the exact ones whenever the frequency separation is smaller than the Fourier resolution limit, Based on the asymptotic results, it is found that the threshold SNR at which an unbiased estimator can resolve the two signal frequencies is at least proportional to ( N . delta w )(-6)/N for the worst phase difference case and to ( N . delta w )(-4)/N for the best phase difference case for small delta w. The results are applicable to the general case of sampling where the samples are taken at arbitrary instants.
dc.identifier.citationDilaveroğlu, E. (1998). "Nonmatrix cramer-rao bound expressions for high-resolution frequency estimators". IEEE Transactions on Signal Processing, 46(2), 463-474.
dc.identifier.endpage474
dc.identifier.issn1053-587X
dc.identifier.issue2
dc.identifier.scopus2-s2.0-0032000282
dc.identifier.startpage463
dc.identifier.urihttps://doi.org/10.1109/78.655430
dc.identifier.urihttps://ieeexplore.ieee.org/document/655430
dc.identifier.urihttp://hdl.handle.net/11452/20900
dc.identifier.volume46
dc.identifier.wos000071871700016
dc.indexed.scopusScopus
dc.language.isoen
dc.publisherIEEE
dc.relation.journalIEEE Transactions on Signal Processing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectClosely spaced sinusoids
dc.subjectSignals
dc.subjectSimple approximations
dc.subjectEngineering
dc.subject.wosEngineering, electrical & electronic
dc.titleNonmatrix cramer-rao bound expressions for high-resolution frequency estimators
dc.typeArticle
dc.wos.quartileQ1
dspace.entity.typePublication
local.contributor.departmentMühendislik Fakültesi/Elektronik Mühendisliği Bölümü
local.indexed.atWOS
local.indexed.atScopus

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