Application Areas

Discrete Wavelet Packet Transform (DWPT) 

In[1]:=

X f[t_] := N[ 4/(1 + Exp[-6.4 t + 3.2]) + Cos[100 \[Pi] t] Ii[t, 1/3, 2/3]]; Ii[t_, x1_, x2_] := Piecewise[{{1, t >= x1 && t <= x2}}, 0]

In[2]:=

X data = Join[Table[f[x], {x, 0, 1, 1/127}], Reverse[Table[f[x], {x, 0, 1, 1/127}]]];

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X dwpt = DiscreteWaveletPacketTransform[data, Automatic, 2];

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X Column[{Show[dwpt["TreeView"], ImageSize -> 300, AspectRatio -> 1/GoldenRatio, PlotLabel -> Style["DWPT Decomposition Tree", FontFamily -> "Verdana", Brown, Bold, 16]], WaveletListPlot[dwpt, All, DataRange -> {0, 1}, Joined -> False, ImageSize -> 570, PlotRangePadding -> None, Filling -> Axis, TicksStyle -> Directive[FontFamily -> "Verdana", 12], PlotMarkers -> "", PlotLabel -> Style["Wavelet Decomposition Plot", FontFamily -> "Verdana", Brown, Bold, 16], Method -> {"PlotData" -> True}, Ticks -> Full, PlotStyle -> (Directive[{Opacity[1], Thickness@0.003, #}] & /@ Append[ConstantArray[ColorData[14][5], 6], ColorData[14][6]]) ]}, Alignment -> Center]

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