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   -> Volume 2, Issue 15


Reply: Question Coeff. for the Chui wavelets, WD 2.14 # 9.
 
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Jaideva C. Goswami, Dept. of Electrical Engineering, Texas A&M Univ.
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PostPosted: Fri Nov 29, 2002 3:37 pm    
Subject: Reply: Question Coeff. for the Chui wavelets, WD 2.14 # 9.
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Reply: Question Coeff. for the Chui wavelets, WD 2.14 # 9.

Note: The equation numbers are from the book, "An Introduction to Wavelets",
by C. K. Chui.

For Chui-Wang wavelets, the reconstruction sequences ({p_k},{q_k}) are
finite but the decomposition sequences ({a_k},{b_k}) are infinite with
exponential decay. Symbols of the decomposition sequences are related
to those of reconstruction sequences through (5.4.12). More explicit
relation is given by (6.5.1). Euler-Frobenius Laurent series that appears
in (6.5.1) is easy to compute for any order of spline (see 6.1.13). Then
the decomposition sequence can be obtained by comparing the corresponding
coefficients of powes of "z" on the both sides of (6.5.1). For this
purpose, use of symbolic computation package such as, MACSYMA, MAPLE, is
advisable.

Another simpler way of computing ({a_k},{b_k}) is given in Prof. Chui's
forthcoming book, "Wavelets: For Time-Frequency Analysis".

Jaideva C. Goswami
Dept. of Electrical Engineering
Texas A&M University
College Station, TX 77840 goswami@ee.tamu.edu
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