Uncertainty Propagation in the Fast Fourier Transform
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918047240945664 |
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| author | Schmid, Luca Muth, Charlotte Schmalen, Laurent |
| author_facet | Schmid, Luca Muth, Charlotte Schmalen, Laurent |
| contents | We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian inference using belief propagation (BP) and expectation propagation, extending its applicability beyond Gaussian assumptions. By leveraging an appropriate BP message representation and a suitable schedule, our method achieves stable convergence with accurate mean and variance estimates. Numerical experiments in representative scenarios from communications demonstrate the practical potential of the proposed framework for uncertainty-aware inference in probabilistic systems operating across both time and frequency domain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty Propagation in the Fast Fourier Transform Schmid, Luca Muth, Charlotte Schmalen, Laurent Machine Learning Signal Processing We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian inference using belief propagation (BP) and expectation propagation, extending its applicability beyond Gaussian assumptions. By leveraging an appropriate BP message representation and a suitable schedule, our method achieves stable convergence with accurate mean and variance estimates. Numerical experiments in representative scenarios from communications demonstrate the practical potential of the proposed framework for uncertainty-aware inference in probabilistic systems operating across both time and frequency domain. |
| title | Uncertainty Propagation in the Fast Fourier Transform |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2504.10136 |