We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accounting for nonstationarity. Moreover, we prove that this estimate lives in a symmetric fractional spline space and give a practical implementation for optimal upsampling of noisy fBm samples by integer factors.
Type
conference paper
Publication date
2006
Publisher
Published in
Proceedings of the Thirty-First IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'06)
Issue
Toulouse, French Republic
Start page
III
End page
860
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
September 18, 2015
Use this identifier to reference this record