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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.18456 |
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| _version_ | 1866910919061143552 |
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| author | Wahlberg, Patrik |
| author_facet | Wahlberg, Patrik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Filtering of second order generalized stochastic processes corrupted by additive noise Wahlberg, Patrik Functional Analysis Information Theory Probability 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. |
| title | Filtering of second order generalized stochastic processes corrupted by additive noise |
| topic | Functional Analysis Information Theory Probability |
| url | https://arxiv.org/abs/2504.18456 |