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   -> Volume 3, Issue 8

Answer: WD 3.7 #9
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Author Message (Mladen Victor Wickerhauser)

PostPosted: Mon Dec 02, 2002 1:06 pm    
Subject: Answer: WD 3.7 #9
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Answer: WD 3.7 #9

In wavelet digest 3.7, you wrote:

In the document Ten Lectures on Wavelets by Ingrid Daubechies, 1992
Tables 8.2 (page 277) and 8.3 (page 279), the coefficients taken for
Synthesis (inverse) filter to be the m_0^tilde filter, seem NOT to
produce exact reconstruction? for DBS(3,7).

There is a transposition of two digits in one of the coefficients of the
(3,7) biorthogonal quadrature filter. Here are the correct coefficients:

[ SR2OVER2E14 is sqrt(2.0)/(1<<14); in Daubechies'
normalization, you don't need the sqrt(2.0) ]

Low-pass High-pass
-------- ---------
35.0*SR2OVER2E14 -35.0*SR2OVER2E14
-105.0*SR2OVER2E14 -105.0*SR2OVER2E14
-195.0*SR2OVER2E14 195.0*SR2OVER2E14
865.0*SR2OVER2E14 865.0*SR2OVER2E14
363.0*SR2OVER2E14 -363.0*SR2OVER2E14
-3489.0*SR2OVER2E14 -3489.0*SR2OVER2E14
-307.0*SR2OVER2E14 307.0*SR2OVER2E14
11025.0*SR2OVER2E14 11025.0*SR2OVER2E14
11025.0*SR2OVER2E14 -11025.0*SR2OVER2E14
-307.0*SR2OVER2E14 -307.0*SR2OVER2E14
-3489.0*SR2OVER2E14 3489.0*SR2OVER2E14
363.0*SR2OVER2E14 363.0*SR2OVER2E14
865.0*SR2OVER2E14 -865.0*SR2OVER2E14
-195.0*SR2OVER2E14 -195.0*SR2OVER2E14
-105.0*SR2OVER2E14 105.0*SR2OVER2E14
35.0*SR2OVER2E14 35.0*SR2OVER2E14

Professor Mladen Victor Wickerhauser <>
Department of Mathematics, Campus Box 1146, One Brookings Drive
Washington University in Saint Louis, Missouri 63130 USA
Telephone: USA+(314)935-6771; Facsimile: USA+(314)935-5799
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