Signal detection in fractional Gaussian noise
- 1 September 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 34 (5) , 943-959
- https://doi.org/10.1109/18.21218
Abstract
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.<>Keywords
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