Uncertainty Propagation in the Fast Fourier Transform
This addresses uncertainty propagation in Fourier transforms for probabilistic systems in communications, representing an incremental advancement.
The paper tackles the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph, proposing an efficient framework for approximate Bayesian inference using belief propagation and expectation propagation. Numerical experiments in communications scenarios demonstrate the framework's practical potential for uncertainty-aware inference in probabilistic systems across time and frequency domains.
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.