Spectrum estimation is a fundamental methodology in the analysis of time-series data, with applications including medicine, speech analysis, and control design. The asymptotic theory of spectrum estimation is well-understood, but the theory is limited when the number of samples is fixed and finite. This paper gives non-asymptotic error bounds for a broad class of spectral estimators, both pointwise (at specific frequencies) and in the worst case over all frequencies. The general method is used to derive error bounds for the classical Blackman-Tukey, Bartlett, and Welch estimators.
翻译:频谱估计是时间序列数据分析中的一种基本方法,应用包括医学、语音分析和控制设计。渐近理论在频谱估计中已经得到了很好的理解,但当样本数量固定且有限时,渐近理论的使用就受到了限制。本文给出了广泛类别频谱估计器的非渐近误差界限,包括点值界限(特定频率)和所有频率的最坏情况界限。使用该通用方法,导出了经典的Blackman-Tukey、Bartlett和Welch估计器的误差界限。