连续小波变换跟其工程运用.pdf
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Daubechies
{h }{g }Mallat
k k
S. G. Mallat A Wavelet Tour of Signal Processing (Second Edition)
Laplace Hermitian
6.1
6.1.1
(harmonic wavelet)D. E. Newland
L2(R)
FFTIFFT
w (t)w (t) ,
e o
1 / 4π 2π ≤ |ω | 4π
⎧
W (ω) = ( 6.1.1 )
e ⎨
⎩ 0
i / 4π − π ≤ ω − π
⎧ 4 2
⎪
W (ω) = − i / 4π 2π ≤ ω 4π ( 6.1.2 )
o ⎨
⎪ 0
⎩
i= − 1 6.1.1 a, b
W (ω) W (ω) W(ω)
e o
1/4π i/4π 1/2π
2π 4π
-4π -2π 0 2π 4π ω -4π -2π 0 ω 0 2π 4π ω
(a) W (ω) (b) W (ω) (c) W (ω)
e o
6.1.1 W (ω), W (ω)W (ω)
e o
139
W (ω) = W (ω) + iW (ω)
e o
1/ 2π 2π ≤ ω 4π
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