Knowledge Notes
知识点：跨模块的基础解释
这里集中解释多个算法都可能用到的知识，不要求先读某个模块。 从算法页遇到概念时可以跳来补充，再通过页内链接返回原来的章节继续读。
FFT、频点与 Nyquist 频率：从时域波形、频谱和复平面图理解 FFT 输出的振幅与相位，以及采样的频率限制。
谱泄漏与窗函数：用周期拼接图和频谱比较图理解 “不在频点上”的单频信号为什么会出现在很多频点中。
窄带相位的省点计算：把频带搬到低频，用较少时刻计算慢相位， 再还原到原采样点；配有移频图、误差图和 Python 示例。
应用入口：探针诊断基础。
Knowledge notes: foundations shared by algorithm modules
These notes explain concepts used across algorithms without requiring a particular module. Follow a concept link from an algorithm page, then use the return link to resume its section.
FFT, frequency bins, and the Nyquist frequency: connect time traces, spectra, and complex-plane diagrams to amplitude, phase, and sampling limits.
Spectral leakage and windows: use repeated-record and spectrum plots to see why an off-bin tone contributes to multiple bins.
Fewer-point evaluation of narrowband phase: shift a band to low frequencies, evaluate slow phase on fewer time points, and restore the original sampling grid, with frequency-shift plots, error plots, and Python examples.
Application: Probe Diagnostics Foundations.