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Estimation of frequencies of sinusoids in the presence of noise
Author(s) -
Ong B. G.,
Campbell L. L.
Publication year - 1979
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315010
Subject(s) - estimator , noise (video) , mathematics , gaussian noise , statistics , variance (accounting) , gaussian , covariance matrix , covariance , simple (philosophy) , algorithm , computer science , physics , artificial intelligence , accounting , quantum mechanics , business , image (mathematics) , philosophy , epistemology
A method is proposed and developed for estimating the frequencies of K sinusoids given the sum of these sinusoids in Gaussian noise. Attention is focused on the properties of these estimators when the observation time is short, the separation between frequencies is small, and the signal‐to‐noise ratio is high. The estimators are shown to be approximately unbiased and approximately normally distributed. The covariance matrix is also calculated. Relatively simple bounds on the variance of the estimators are found.