Bertrand's Representation of the Optimal Detector

Vladimir Lenok

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arXiv · 2509.10198

Bertrand's Representation of the Optimal Detector

Vladimir Lenok

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Abstract

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.

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Vladimir Lenok. 2025-09-12. Bertrand's Representation of the Optimal Detector. https://arxiv.org/abs/2509.10198

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