Signal detection in fractional Gaussian noise

Several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented to facilitate the study of signal detection in additive fractional Gaussian noise. This Hilbert space is completely characterized, and an alternative characterization for the restriction of th...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 34; no. 5; pp. 943 - 959
Main Authors Barton, R.J., Poor, H.V.
Format Journal Article
LanguageEnglish
Published IEEE 01.09.1988
Subjects
1f noise
Additive noise
Brownian motion
Communication channels
Frequency
Gaussian noise
Hilbert space
Kernel
Oscillators
Signal detection
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Summary:Several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented to facilitate the study of signal detection in additive fractional Gaussian noise. This Hilbert space is completely characterized, and an alternative characterization for the restriction of this class of functions to a compact interval (0.T) is given. Infinite- and finite-interval whitening filters for fractional Brownian motion are also developed. The application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional Gaussian noise. A formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed.< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/18.21218