2D DWT basis function examples

Haar example

haar = HaarFilter[]

RowBox[{{, RowBox[{0.707107, ,, 0.707107}], }}]

dim = 64 ; which = {6, 6} ;

tmp = InverseWaveletTransform2D[ReplacePart[Table[0, {dim}, {dim}], 1, which], haar, 7] ; ListPlot3D[tmp, MeshFalse, PlotRangeAll, ImageSize500] ;

[Graphics:../HTMLFiles/index_426.gif]

Daubechies-4 example

db4 = DaubechiesFilter[4]

RowBox[{{, RowBox[{0.482962913144534143375, ,, 0.83651630373780790558, ,, 0.22414386804201338103, ,, RowBox[{-, 0.12940952255126038117}]}], }}]

dim = 64 ; which = {6, 6} ;

tmp = InverseWaveletTransform2D[ReplacePart[Table[0, {dim}, {dim}], 1, which], db4, 7] ; ListPlot3D[tmp, MeshFalse, PlotRangeAll, ImageSize500] ;

[Graphics:../HTMLFiles/index_431.gif]

Daubechies-8 example

db8 = DaubechiesFilter[8]

RowBox[{{, RowBox[{0.23037781330889650086, ,, 0.71484657055291564709, ,, 0.6308807679298589079 ... , 0.0308413818355607636, ,, 0.03288301166688519974, ,, RowBox[{-, 0.010597401785069032105}]}], }}]

dim = 64 ; which = {7, 7} ;

tmp = InverseWaveletTransform2D[ReplacePart[Table[0, {dim}, {dim}], 1, which], db8, 7] ; ListPlot3D[tmp, MeshFalse, PlotRangeAll, ImageSize500] ;

[Graphics:../HTMLFiles/index_436.gif]

Created by Mathematica  (February 5, 2004)