Introduction to Wavelets part 2. By Barak Hurwitz. Wavelets seminar with Dr ’ Hagit Halor. List of topics. Reminder 1D signals Wavelet Transform CWT,DWT Wavelet Decomposition Wavelet Analysis 2D signals Wavelet Pyramid some Examples. Reminder – from last week.
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Noise
the coarser the signal features being measured by the wavelet coefficient.
Low scale High scale
Solution: choose only a subset of scales and positions, based on power of two (dyadic choice)
Discrete Wavelet Transform
Input Signal
HPF
Approximations and Details:
A complete one stage block :
A*
LPF
Input Signal
D*
HPF
high pass filter
Low pass filter
Up sampling
(or interpolation) is done by zero inserting between every two coefficients
* Wavelet used: db2
What’s wrong with Gabor?
low frequency
scale
Discontinuity effect
time
High frequency
NOTHING!
exact location
in time of the discontinuity.
more
)
)
(
Y
=
Y

x
b
1
a
,
b
x
a
a
2D SIGNALWavelet function
1D function
1D
2D
LENNA
DWTDCT
Wavelet analysis is a new and promising set of tools for analyzing these signals