Wavelet

Introduction to Wavelet Transform

TABLE OF CONTENT ,[object Object],[object Object],[object Object],[object Object]

Time Domain Signal 10 Hz 2 Hz 20 Hz 2 Hz + 10 Hz + 20Hz Time Time Time Time Magnitude Magnitude Magnitude Magnitude

FREQUENCY ANALYSIS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Limitations of FT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Limitations of FT Occur at all times Do not appear at all times Time Magnitude Magnitude Frequency (Hz) 2 Hz + 10 Hz + 20Hz Stationary Time Magnitude Magnitude Frequency (Hz) Non-Stationary 0.0-0.4: 2 Hz + 0.4-0.7: 10 Hz + 0.7-1.0: 20Hz

[object Object],Limitations of FT Same in Frequency Domain ,[object Object],At what time the frequency components occur? FT can not tell! Time Magnitude Magnitude Frequency (Hz) Time Magnitude Magnitude Frequency (Hz) Different in Time Domain

[object Object],[object Object],Limitations of FT Many Signals in our daily life are Non-stationary. (We need to know whether and also when an incident was happened.)

WAVELET TRANSFORM Translation (The location of the window) Scale Window function

SCALE and Translation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

COMPUTATION OF CWT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object],[object Object]

Wavelet

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Wavelet