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Visualizing Wavelet Coefficient Distributions 

In[1]:=

X data = WeatherData["KMDZ", "MeanTemperature", {{2007, 1, 1}, {2007, 12, 31}, "Day"}];

In[2]:=

X plot = DateListPlot[data, Joined -> True, ImageSize -> 412, FrameTicksStyle -> Directive[12, FontFamily -> "Helvetica"], PlotStyle -> ColorData["FallColors"][0]];

In[3]:=

X dwd = StationaryWaveletTransform[data[[All, 2]], HaarWavelet[], 5];

In[4]:=

X bwc = BoxWhiskerChart[ Join[{data[[All, 2]]}, dwd[Automatic, "Values"]], "Notched", ChartLabels -> Placed[Join[{"data"}, dwd["BasisIndex"]], Axis], BarOrigin -> Left, GridLines -> Automatic, ChartStyle -> "FallColors", ImageSize -> 460, FrameTicksStyle -> Directive[12, FontFamily -> "Helvetica"]];

In[5]:=

X Framed[Grid[{{Column[{"Mean", "temperatures"}], plot}, {Column[{"Wavelet", "coefficent", "distribution"}], bwc}}, Alignment -> {{Left, Right}, {Center}}, Dividers -> Center, Spacings -> {1, 3}, FrameStyle -> GrayLevel@0.8, BaseStyle -> {FontFamily -> "Helvetica", 12, Bold}], RoundingRadius -> 10, FrameStyle -> GrayLevel@0.2, FrameMargins -> 10]

Out[5]=