1. Visual Communication Lab
Wavelet in Matlab
Visual Communication Lab
Park Won Bae ‘
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2. Overview #1 - Fourier Analysis
> In transforming to the frequency domain, time information is lost
- STFT(Short Time Fourier Transform)
> Provide some information about both when and at what frequencies
a signal event occurs
> We can only obtain this information with limited precision
- Wavelet Analysis
> long time intervals where we want more precise low frequencies information
> shorter regions where we want high frequencies information
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3. Overview #2
- Wavelet
> a waveform of effectively limited duration that has an average value
of zero
> the breaking up of a signal into shifted and scaled version
of the original(mother) wavelet
> low scale = compressed wavelet = rapidly changing details = High freq.
> high scale = stretched wavelet = slowly changing, coarse = Low freq
> wavelet function and scaling function
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4. Overview #3 - Multi-Step Decomposition and Reconstruction
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5. * Multi-level Wavelet Analysis of a signal #1
- STEP 1 : Performing a Multi-Level Wavelet
Decomposition of a signal ( wavedec )
- STEP 2 : Extracting Approximation and detail
Coefficients ( appcoef, detcoef )
- STEP3 : Reconstructing the Level 3 Approximation
( wrcoef - type ‘a’ )
- STEP4 : Reconstructing the Level 1,2 and 3 Details
(wrcoef - type ‘d’ )
- STEP 5 : Reconstructing the Original from the Level 3 Decomposition
( waverec )
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6. * Multi-level Wavelet Analysis of a signal #2
- wavedec : Multi-level 1-D Wavelet decomposition
[C,L] = wavedec(X,N,’wavelet-name’)
X : signal , N : level
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7. * Multi-level Wavelet Analysis of a signal #3
- appcoef : Extract 1-D approximation coefficients
> A = appcoef(C,L,’wavelet-name’, N)
- detcoef : Extract 1-D detail coefficients
> D = detcoef(C,L,N)
- wrcoef : Reconstruct single branch from 1-D wavelet coeff
> X = wrcoef(‘type’, C,L, ‘wavelet-name’, N)
type : ‘a’ - approximation
‘d’ - detail
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8. < pwb1.m file 참고 >
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9. * 2-D Discrete Wavelet Analysis #1
- dwt2 : Single-level discrete 2-D wavelet transform
[cA,cH,cV,cD] = dwt2(X,’wavelet-name’)
- idwt2 : Single-level inverse discrete 2-D wavelet transform
X = idwt2(cA,cH,cV,cD,’wavelet-name’,S)
S : size(X) = 2*size(cA)-lf+2
( lf : filter lengths)
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10. < Original Image >
< pwb4.m file 참고 >
< Decomposition Image >
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11. * 2-D Discrete Wavelet Analysis #2
- wavedec2 : Multi-level 2-D Wavelet decomposition
[C,S] = wavedec2(X,N, ‘wavelet-name’)
S : bookkeeping matrix
- waverec2 :Multi-level 2-D wavelet reconstruction
X = waverec2(C,S,’wavelet-name’)
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12. * 2-D Discrete Wavelet Analysis #3
- appcoef2 : Extract 2-D approximation coefficients
> A = appcoef2(C,S,’wavelet-name’, N)
- detcoef2 : Extract 2-D detail coefficients
> D = detcoef2(O,C,S,N)
O : Direction ‘h’,’v’,’d’
- wrcoef2 : Reconstruct single branch from 2-D wavelet coeff
> X = wrcoef2(‘type’, C,S, ‘wavelet-name’, N)
type : ‘a’ - approximation
‘h’,’v’,’d’ - reconstruction
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