梳理频域时间序列分析的挑战与前沿，提供方法选型框架
Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks
- 构建频域分析统一分类体系，融合经典与神经网络方法
- 识别出因果性保持、不确定性量化等三大核心难题
- 为非欧数据结构分析提供新思路，适合领域研究者参考
频域分析已成为时间序列分析的强大范式，相较于传统时域方法具有独特优势，同时也带来新的理论与实践挑战。本文系统综述了从经典傅里叶分析到现代神经算子的谱方法，梳理当前研究中的三大开放问题：（1）频域变换中因果结构的保持；（2）学习型频域表示的不确定性量化；（3）非欧数据结构的拓扑感知分析。通过严格评审100余篇文献，建立统一分类体系，贯通传统谱技术与前沿机器学习方法，并制定标准化评估基准。研究揭示了几何深度学习与量子增强频域分析中的关键知识缺口。本工作为从业者提供系统的方法选择与实现框架，指明该快速演进领域的未来方向。
原文摘要 · Abstract (English)
Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a comprehensive examination of spectral methods from classical Fourier analysis to modern neural operators, systematically summarizing three open challenges in current research: (1) causal structure preservation during spectral transformations, (2) uncertainty quantification in learned frequency representations, and (3) topology-aware analysis for non-Euclidean data structures. Through rigorous reviewing of over 100 studies, we develop a unified taxonomy that bridges conventional spectral techniques with cutting-edge machine learning approaches, while establishing standardized benchmarks for performance evaluation. Our work identifies key knowledge gaps in the field, particularly in geometric deep learning and quantum-enhanced spectral analysis. The survey offers practitioners a systematic framework for method selection and implementation, while charting promising directions for future research in this rapidly evolving domain.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。