用因子图建模FFT，实现非高斯条件下的不确定度传播。
Uncertainty Propagation in the Fast Fourier Transform
- 将FFT视为因子图，用变分推断进行不确定性传播
- 在通信场景中实现稳定收敛，均值与方差估计准确
- 适合需要时频域联合概率推断的系统设计
针对离散傅里叶变换中的不确定度传播问题，本文将快速傅里叶变换（FFT）建模为因子图。基于此表示，提出一种高效近似贝叶斯推断框架，结合信念传播（BP）与期望传播，突破了传统方法对高斯假设的依赖。通过采用合适的BP消息表示与调度策略，该方法实现了稳定的收敛，并获得了精确的均值与方差估计。在通信领域的典型场景中开展的数值实验表明，所提框架在时频域联合概率推断中具有实际应用潜力，可支持不确定性感知的系统分析与设计。
原文摘要 · Abstract (English)
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.
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