Walsh-Fourier Analysis and Its Statistical Applications
本文向统计学家和从业者介绍沃尔什-傅里叶分析的统计理论与应用，特别适用于离散值、分类值或含尖锐间断的时间序列分析，并提供了相关文献注释。
Abstract The aim of this article is to acquaint statisticians and practitioners, whose research activities require statistical methodology, with the statistical theory and applications of Walsh-Fourier analysis. It has been suggested that Walsh spectral analysis is suited to (albeit not restricted to) the analysis of discrete-valued and categorical-valued time series, and of time series that contain sharp discontinuities. I explain the need for Walsh-Fourier analysis, review the history and properties of Walsh functions, and outline the existing Walsh-Fourier theory for real-time stationary time series. I discuss various statistical applications based on the Walsh-Fourier transform and provide an annotated bibliography.