Wavelet Transform for Orthogonal Daubechies Wavelets

To show the differences, first just the nodal values are wavelet transformed. In the second part of the code scaling function coefficients are computed from nodal values via a quadrature rule [2]. Then these coefficients are transformed. The source to this example is Sources/Examples/WTDaub.cc. You can compile it by

see the code WTDaub.cc

WTDaub.exe produces two files which contain wavelet coefficients.
Visualize the results in MATLAB by (AWFD/Sources/Examples/wtdaub.m)

`A=ReadUDF('../../Data/Test/Bd1') ;
B=ReadUDF('../../Data/Test/Bd2') ;
figure(1);
pcolor(log(abs(A.a))) ;shading flat;
set(gca,'ZLim',[-30,2.5]);
set(gca,'FontSize',20);
set(gca,'XTick',[]) ;
set(gca,'YTick',[]) ;
title 'without quadrature'
figure(2);
pcolor(log(abs(B.a))) ;shading flat;
set(gca,'ZLim',[-30,2.5]);
set(gca,'FontSize',20);
set(gca,'XTick',[]) ;
set(gca,'YTick',[]) ;
title 'with quadrature'
`

You should get the following two figures. The first figure shows the wavelet coefficients when no quadrature has been used. The second figure show sthe coefficients if a quadrature has been used. In the first case, there are large wavelets coefficients even at higher levels. This diminishes the effectivity of e.g. wavelet compression, see [2] for a discussion on this. In the second case, this problem is still present, but much weaker.