1D DWT basis function examples

Haar wavelets

Haar low-pass filter

haar = HaarFilter[]

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

Haar high-pass filter

HighPassFilter[haar]

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

Example Haar-wavelet basis functions

zeros = Table[0, {128}] ;

Table[ListPlot[InverseWavelet1D[ReplacePart[zeros, 1, i], haar], PlotRangeAll, PlotJoi ... 54;True, PlotStyle {Red, Thickness[.005]}, ImageSize288], {i, 1, Length[zeros]}] ;

[Graphics:../HTMLFiles/index_135.gif]

(Web: click on image to see all 64 basis functions)

Daubechies-4 wavelets

Daubechies low-pass filter

db4 = DaubechiesFilter[4]

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

Daubechies high-pass filter

HighPassFilter[db4]

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

Example Daubechies-wavelet basis functions

zeros = Table[0, {128}] ;

Table[ListPlot[InverseWavelet1D[ReplacePart[zeros, 1, i], db4], PlotRangeAll, PlotJoin ... 54;True, PlotStyle {Red, Thickness[.005]}, ImageSize288], {i, 1, Length[zeros]}] ;

[Graphics:../HTMLFiles/index_270.gif]

(Web: click on image to see all 64 basis functions)

Daubechies-8 wavelets

Daubechies low-pass filter

db8 = DaubechiesFilter[8]

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

Daubechies high-pass filter

HighPassFilter[db8]

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

Example Daubechies-wavelet basis functions

zeros = Table[0, {128}] ;

Table[ListPlot[InverseWavelet1D[ReplacePart[zeros, 1, i], db8], PlotRangeAll, PlotJoin ... 54;True, PlotStyle {Red, Thickness[.005]}, ImageSize288], {i, 1, Length[zeros]}] ;

[Graphics:../HTMLFiles/index_405.gif]

(Web: click on image to see all 64 basis functions)

Created by Mathematica  (February 5, 2004)