Wavelet tutorial part 1 小结

Part 1

Fundamental Concepts and an Overview of the Wavelet Theory

1. 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.

2. The FT gives what frequency components (spectral components) exist in the signal. Nothing more, nothing less.

3. Time-frequency representation can provide time localization information.

The Ultimate Solution: The Wavelet Transform

1. 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.

2. 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.