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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.)
Solutions = Wavelet Transform
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]
S = 5
S = 20
COMPUTATION OF CWT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object]
End

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