Chapter 2 Tight-frames An Introduction 1 Outline 1. Tight-frame - - PDF document
Chapter 2 Tight-frames An Introduction 1 Outline 1. Tight-frame 1. Tight-frame 2. Matrix Representation 2. Matrix Representation 2 1 Tight Frames 3 Construction of Haar Wavelet = + 4 2 Construction of Haar Wavelet 5 Construction
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−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
Piecewise Linear Refinable Function φ
−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
φ(2x+1) /2 φ(2x−1) /2 φ (2x) φ(x)=φ(2x+1)/2+φ(2x)+φ(2x−1)/2
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−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
Piecewise Linear Refinable Function φ
−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8
0.707φ(2x+1) −0.707φ(2x−1) ψ1(x)=0.707φ(2x+1)−0.707φ(2x−1)
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−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
Piecewise Linear Refinable Function φ
−1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 0.8 1 −0.4 −0.2 0.2 0.4 0.6 0.8 1
−φ(2x+1)/2 −φ(2x−1) /2 φ(2x) ψ2(x)=−φ(2x+1)/2+φ(2x)−φ(2x−1)/2
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