This investigation establishes the theoretical and practical limits of signal strength estimate precision for Kolmogorov-Zurbenko periodograms with dynamic smoothing and compares them to those of standard log-periodograms with static smoothing. Previous research has established the sensitivity, accuracy, resolution, and robustness of Kolmogorov-Zurbenko periodograms with dynamic smoothing in estimating signal frequencies. However, the precision with which they estimate signal strength has never been evaluated. To this point, the width of the confidence interval for a signal strength estimate can serve as a criterion for assessing the precision of such estimates: the narrower the confidence interval, the more precise the estimate. The statistical background for confidence intervals of periodograms is presented, followed by candidate functions to compute and plot them when using Kolmogorov-Zurbenko periodograms with dynamic smoothing. Given an identified signal frequency, a static smoothing window and its smoothing window width can be selected such that its confidence interval is narrower and, thus, its signal strength estimate more precise, than that of dynamic smoothing windows, all while maintaining a level of frequency resolution as good as or better than that of a dynamic smoothing window. These findings suggest the need for a two-step protocol in spectral analysis: computation of a Kolmogorov-Zurbenko periodogram with dynamic smoothing to detect, identify, and separate signal frequencies, followed by computation of a Kolmogorov-Zurbenko periodogram with static smoothing to precisely estimate signal strength and compute its confidence intervals.

翻译：本研究确立了动态平滑Kolmogorov-Zurbenko周期图在信号强度估计精度方面的理论与实际极限，并将其与采用静态平滑的标准对数周期图的性能进行对比。先前研究已证实动态平滑Kolmogorov-Zurbenko周期图在信号频率估计方面具有灵敏度、准确性、分辨率和鲁棒性优势，但其信号强度估计的精度尚未得到评估。在此背景下，信号强度估计的置信区间宽度可作为评估此类估计精度的标准：置信区间越窄，估计精度越高。本文首先阐述周期图置信区间的统计学背景，继而提出适用于动态平滑Kolmogorov-Zurbenko周期图的置信区间计算与绘制候选函数。在已识别信号频率的前提下，通过选择特定静态平滑窗口及其窗宽，可在保持频率分辨率不低于动态平滑窗口的同时，获得比动态平滑窗口更窄的置信区间，从而实现更精确的信号强度估计。这些发现表明谱分析需要采用两步流程：首先通过动态平滑Kolmogorov-Zurbenko周期图实现信号频率的检测、识别与分离，继而采用静态平滑Kolmogorov-Zurbenko周期图精确估计信号强度并计算其置信区间。