这篇博客探讨了傅立叶变换在处理非平稳信号时的局限性，指出其无法显示不同频率信号的出现时间。时间-频率表示提供了解决这一问题的方法，通过时间局部化信息来展示信号的变化。文章接着介绍了小波变换，它结合了窄窗和宽窗的优点，能够在保持时间分辨率的同时提高频率分辨率。窄窗对应于高频率，宽窗对应于低频率，而窗的宽度（如a=0.01和a=0.0001）决定了时间-频率分辨率的平衡。
Part 1
Fundamental Concepts and an Overview of the Wavelet Theory
-
TF can be used with stationary signal, however there are drawbacks when dealing with nonstationary signal: frequency spectrum can’t show the appearing time of different signals with different frequency.
-
The FT gives what frequency components (spectral components) exist in the signal. Nothing more, nothing less.
-
Time-frequency representation can provide time localization information.
The Ultimate Solution: The Wavelet Transform
- 窄窗：时间分辨率好，频率分辨率差，适合高频率
宽窗：时间分辨率差，频率分辨率好，适合低频率
For the same time interval, longer interval can present more points for low frequency signal.
- Uncertainty principle: we cannot exactly know the frequency and its time localization simultaneously. We can only know the frequency bands and its time interval
Question:
为什么a=0.01为窄窗，a=0.0001则为宽窗？
To be continued.
扫一扫
966
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
