On estimating spectral moments in the presence of colored noise

Author

Miller, Kenneth S. ; Rochwarger, Marvin M.

Volume

Issue

fYear

1970

fDate

5/1/1970 12:00:00 AM

Firstpage

303

Lastpage

309

Abstract

Let ${q^(1) (t)}$ , the signal, be a complex Gaussian process corrupted by additive Gaussian noise ${q^(2) (t) }$ . Observations on $p(t)q(t)$ and $p(t) q^(2) (t)$ are assumed to be available where $p(t)$ is a smooth weighting function and $q = q^(1) + q^(2)$ . Using the Fourier transform of the samples of $p(t)q(t)$ and $p(t) q^(2) (t)$ , estimators are derived for estimating the mean frequency and spectral width of the unknown power spectrum of the unweighted signal process. The means and variances of these statistics are computed in general, and explicitly for nontrivial practical examples. Asymptotic formulas for the moment estimators as a function of the number of realizations, frequency resolution, signal-to-noise ratio and spectral width, and consistency of the estimators are some of the results that are discussed in detail.

Keywords

Spectral analysis; Additive noise; Colored noise; Fourier transforms; Frequency estimation; Gaussian noise; Gaussian processes; Signal processing; Signal resolution; Signal to noise ratio; Statistics;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1970.1054460

Filename

1054460

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=913902