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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.10198 |
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| _version_ | 1866909783864377344 |
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| author | Lenok, Vladimir |
| author_facet | Lenok, Vladimir |
| contents | It is shown how the optimal detector of Gaussian signals can be represented in terms of Bertrand's class of time-frequency distributions. In this representation, the detector is a correlation between the corresponding time-frequency distributions. Since Bertrand's class is related to the power-law chirp signals, the new representation can be useful for their detection. The new approach is shown to be more effective then other time-frequency methods for the case of phase-insensitive detection. The finding provides a complementary representation to Cohen's class representation in the time-frequency domain already known in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bertrand's Representation of the Optimal Detector Lenok, Vladimir Data Analysis, Statistics and Probability Instrumentation and Methods for Astrophysics It is shown how the optimal detector of Gaussian signals can be represented in terms of Bertrand's class of time-frequency distributions. In this representation, the detector is a correlation between the corresponding time-frequency distributions. Since Bertrand's class is related to the power-law chirp signals, the new representation can be useful for their detection. The new approach is shown to be more effective then other time-frequency methods for the case of phase-insensitive detection. The finding provides a complementary representation to Cohen's class representation in the time-frequency domain already known in the literature. |
| title | Bertrand's Representation of the Optimal Detector |
| topic | Data Analysis, Statistics and Probability Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2509.10198 |