A stochastical limit to the resolution of least squares estimation of the frequencies of a double complex sinusoid

Author

Van hamme, Hugo

Author_Institution

Dept. ELEC, Vrije Univ., Brussel, Brussels, Belgium

Volume

39

Issue

12

fYear

1991

fDate

12/1/1991 12:00:00 AM

Firstpage

2652

Lastpage

2658

Abstract

A theory of degeneracy of the parameter estimation problem for two complex sinusoids from noisy observations is presented. It is shown that some noise realization may perturb the least-squares cost function such that the frequencies cannot be resolved. In that case, a linearly modulated complex sinusoid provides the best fit to the data. The phenomenon is shown to be more important than the well-known threshold effect. An approximate expression for the probability of degeneration is derived and verified through simulation for the case of white Gaussian noise

Keywords

least squares approximations; parameter estimation; signal processing; stochastic processes; degeneracy theory; degeneration probability; double complex sinusoid; frequency estimation; least squares estimation; least-squares cost function; linearly modulated complex sinusoid; noisy observations; parameter estimation; simulation; stochastical limit; white Gaussian noise; Bismuth; Chirp modulation; Cost function; Frequency estimation; Gaussian noise; Least squares approximation; Least squares methods; Noise measurement; Signal generators; Student members;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.107415

Filename

107415