Wavelet tutorial part 2 小结

Fundamentals

FT is not suitable for non-stationary signals.

The Fourier transform

Refer to notes of Fourier transform.

Sudden change of signal will generate noise in the result of TF.

The short time Fourier transform (STFT)

According to Uncertainty principle, when increasing resolution of frequency, time resolution will decrease.

TF gives out best resolution in frequency, but 0 resolution in time. Time domain vice versa. STFT only provide the frequency band in the time interval.

Narrow window: good time resolution, poor frequency resolution. Suitable for high frequency signal.

Wide window: good frequency resolution, poor time frequency resolution. Suitable for low frequency signal.

Question: a 是怎么影响窗宽的？a越大窗宽越小吗？ 图中横纵坐标都没有变化，如何体现窗的宽窄？