Uncertainty Propagation in the Fast Fourier Transform

2025-04-14

AI Summary

This work addresses the challenge of propagating uncertainty between the time and frequency domains in discrete Fourier transforms (DFT). We propose a factor graph–based framework for quantifying uncertainty in the fast Fourier transform (FFT), explicitly modeling FFT as a hierarchical factor graph for the first time. By integrating belief propagation (BP) with expectation propagation (EP), the framework enables approximate Bayesian inference under non-Gaussian priors. A convergence-guaranteeing mechanism ensures stable, high-accuracy joint estimation of posterior means and variances. Unlike conventional approaches constrained by Gaussian assumptions, our method significantly improves the accuracy and robustness of joint time–frequency probabilistic inference—particularly in communication systems. It establishes a scalable theoretical and algorithmic foundation for uncertainty-aware signal processing.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

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.

Problem

• Modeling FFT as factor graph for uncertainty propagation
• Efficient Bayesian inference using belief propagation methods
• Accurate uncertainty-aware inference in time-frequency domains

Innovation

• Model FFT as factor graph for uncertainty propagation
• Use belief propagation for Bayesian inference
• Achieve stable convergence with accurate estimates