In this “Lecture Notes” column, we show that it is possible to use deterministic arguments to gain some intuition into why using periodograms without averaging does not work well and why they “fail” in the way they do. We then explain how the probabilistic case can be seen as an extension of the deterministic case. Next, we give a brief description of the method of averaged periodograms and explain how the deterministic perspective points to additional cases where the method of averaged periodograms should prove effective. Finally, we provide several numerical examples to demonstrate the theoretical material, and “A Probabilistic Argument” provides a fairly detailed probabilistic justification that is an extension of the deterministic one.

中文翻译：

---

周期图和平均周期图的方法[讲座笔记]

在本“讲义”专栏中，我们展示了可以使用确定性论证来直观地了解为什么使用周期图而不进行平均效果不佳，以及为什么它们会以这种方式“失败”。然后我们解释如何将概率情况视为确定性情况的扩展。接下来，我们简要描述平均周期图方法，并解释确定性观点如何指出平均周期图方法应证明有效的其他情况。最后，我们提供了几个数值例子来证明理论材料，“概率论证”提供了相当详细的概率论证，这是确定性论证的延伸。