Application Areas

Stationary Wavelet Transform (SWT) 

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 swt = StationaryWaveletTransform[Table[f[x], {x, 0, 1, 1/255}], Automatic, 3];

In[3]:=

X Column[{Show[swt["TreeView"], ImageSize -> 300, AspectRatio -> 1/GoldenRatio, PlotLabel -> Style["SWT Decomposition Tree", FontFamily -> "Verdana", Brown, Bold, 16]], WaveletListPlot[swt, Automatic, 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[Darker[RGBColor[0.9, 0.7, 0.2]], 4], RGBColor[0.5, 0.2, 0]]) ]}, Alignment -> Center]

Out[3]=