Application Areas

Visualize Scalograms in Three Dimensions 

In[1]:=

X background = Black; cfunc = ColorData["AvocadoColors"];

In[2]:=

X data1 = Table[ Piecewise[{{Sin[2 \[Pi] 10 t], 0 <= t < 1/4}, {Sin[2 \[Pi] 25 t], 1/4 <= t < 1/2}, {Sin[2 \[Pi] 50 t], 1/2 <= t < 3/4}, {Sin[2 \[Pi] 100 t], 3/4 <= t <= 1}}], {t, 0, 1, 1/1023}];

In[3]:=

X cwd1 = ContinuousWaveletTransform[ArrayPad[data1, 8], DGaussianWavelet[5], {Automatic, 12}];

In[4]:=

X ga1 = WaveletScalogram[cwd1, {2 | 3 | 4 | 5 | 6 | 7 | 8 | 9, _}, ColorFunction -> cfunc, Axes -> None, ImageSize -> 280, Background -> background];

In[5]:=

X gb1 = ListPlot3D[ Abs[cwd1[{2 | 3 | 4 | 5 | 6 | 7 | 8 | 9, _}, "Values"]], PlotRange -> All, Mesh -> None, ColorFunction -> cfunc, Boxed -> False, ImageSize -> 280, Axes -> False, Background -> background];

In[6]:=

X d = Re[Zeta[1/2 + I Range[0, 100, 0.01]]];

In[7]:=

X data2 = Table[Sign[Cos[x^2]], {x, -6, 6, 12./1023}];

In[8]:=

X cwd2 = ContinuousWaveletTransform[ArrayPad[data2, 8], Automatic, {11, 12}];

In[9]:=

X ga2 = WaveletScalogram[ cwd2, {2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11, _}, Abs[Re[#1]] &, ColorFunction -> cfunc, Axes -> None, ImageSize -> 280, Background -> background];

In[10]:=

X gb2 = ListPlot3D[ Abs[Re[cwd2[{2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11, _}, "Values"]]], PlotRange -> All, Mesh -> None, ColorFunction -> cfunc, Boxed -> False, ImageSize -> 280, Axes -> False, Background -> background];

In[11]:=

X Grid[{{ga1, gb1}, {gb2, ga2}}, Background -> background]

Out[11]=