Filtering of second order generalized stochastic processes corrupted by additive noise
Functional Analysis
2025-04-28 v1 Information Theory
math.IT
Probability
Abstract
We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operators. We study both the wide-sense stationary case and the non-stationary case. In the former case the equation simplifies into a convolution equation. The solution is the Radon--Nikodym derivative between non-negative tempered Radon measures, for signal and signal plus noise respectively, in the frequency domain. In the non-stationary case we work with pseudodifferential operators with symbols in Sj\"ostrand modulation spaces which admits the use of its spectral invariance properties.
Cite
@article{arxiv.2504.18456,
title = {Filtering of second order generalized stochastic processes corrupted by additive noise},
author = {Patrik Wahlberg},
journal= {arXiv preprint arXiv:2504.18456},
year = {2025}
}
Comments
35 pages