Embed Size (px)
Citation preview
Wavelet Transform
Presented byImane Hafnaoui
Fourrier Transform Limitations
FT shows what frequencies exist in a signal.
0 0.2 0.4 0.6 0.8 1-3
-2
-1
0
1
2
3
0 5 10 15 20 250
100
200
300
400
500
600
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)
2 Hz + 10 Hz + 20Hz
Stationary
• FT is not good with non-stationary signals
0 0.2 0.4 0.6 0.8 1-3
-2
-1
0
1
2
3
0 5 10 15 20 250
100
200
300
400
500
600
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)
2 Hz + 10 Hz + 20Hz
Stationary
0 0.5 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
50
100
150
200
250
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)
Non-Stationary
0.0-0.4: 2 Hz + 0.4-0.7: 10 Hz + 0.7-1.0: 20Hz
• FT only shows how much of each frequency is present but not at what time it occurs.
0 0.5 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
50
100
150
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)0 0.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
50
100
150
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)
Different in Time Domain
Same in Frequency Domain
Problem• Time – Frequency representation is
needed.
SolutionWavelet Transform
Wavelet Transform
dts
ttx
sss xx
1
, ,CWT
Mother Wavelet
Translation Scale
Applications
• Image Compression• Signal De-noising• Edge and Rupture detection
