This paper studies classes of nonstationary processes, such as warped processes and frequency-modulated processes, that result from the deformation of stationary processes. Estimating deformations can often provide important information about an underlying physical phenomenon. A computational harmonic analysis viewpoint shows that the deformed autocovariance satisfies a transport equation at small scales, with a
velocity proportional to a deformation gradient. We derive an estimator of the deformation from a single realization of the deformed process, with a proof of consistency under appropriate assumptions.
Publié le : 2003-12-14
Classification:
Nonstationary processes,
inverse problem,
wavelets,
warping,
frequency modulation,
scalogram,
spectrogram,
62M10,
60G12,
60G35
@article{1074290327,
author = {Clerc, Maureen and Mallat, St\'ephane},
title = {Estimating deformations of stationary processes},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 1772-1821},
language = {en},
url = {http://dml.mathdoc.fr/item/1074290327}
}
Clerc, Maureen; Mallat, Stéphane. Estimating deformations of stationary processes. Ann. Statist., Tome 31 (2003) no. 1, pp. 1772-1821. http://gdmltest.u-ga.fr/item/1074290327/