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32Wavelet(3) - 2(t 1 0-1-2-2-1 0 1 2 t second 2 w(t 1...

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-2 -1 0 1 2 -2 -1 0 1 2 t, second ) ( t φ -2 -1 0 1 2 -2 -1 0 1 2 t, second w(t) -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 0 0.5 1 f, Hz Im[W(f)] Figure 1. Haar scaling function and Haar wavelet with its Fourier transform
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MAE 591 RANDOM DATA C. W. Lee Fig.2 Demonstration of Haar wavelet analysis 1 1 MATLAB > wavemenu
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MAE 591 RANDOM DATA C. W. Lee Table 1. Properties of wavelets Family Haar 2 Daubechies Gaussian 3 Morlet 4 Order = D2= db1 5 N (db N = D2 N ) N Orthogonality Yes Yes No No Compact Support Yes Yes No No DWT/CWT O/O O/O X/O X/O Support Width 1 2 N -1 Infinite Effective [-5 5] Infinite Effective [-4 4] Filters Length 2 2 N Regularity Discontinuous ~0.2 N Symmetry/ Anti-symmetry Yes Far from N even/ N odd Yes # of vanishing moments for w(t) 1 N Remarks - Orthogonal and compactly supported wavelets. - Poor regularity - Crude wavelets (e.g. Mexican hat)
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  • Spring '09
  • .
  • probability density function, Dirac delta function, Wavelet, Discrete wavelet transform, Haar wavelet, C. W. Lee

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