Optimal interpolation of fractional Brownian motion given its noisy samples
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Journal Volume
3
ISBN
142440469X
Date Issued
2006-12-01
Author(s)
Unser, Michael
Abstract
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. © 2006 IEEE.
Type
conference paper