Work

Filtering of Second Order Generalized Stochastic Processes Corrupted by Additive Noise

Year: 2026

Type: article

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 Sjöstrand modulation spaces which admits the use of its spectral invariance properties.

Source: Journal of Fourier Analysis and Applications

DOI: 10.1007/s00041-026-10282-y

Author: Patrik Wahlberg

Institution: Politecnico di Torino

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Torino, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni