File:Continuous wavelet transform.gif

wavelet[x_] := E^(-(x^2/2)) Cos[\[Pi] x]; (*Define your wavelet*)
signal = 1.3 E^(-((x + 3)^2/(2 0.2))) Cos[1.6 \[Pi] x] + 0.5 E^(-((x - 1)^2/(2 2))) Cos[0.5 \[Pi] x] - 0.5 E^(-((x + 0)^2/(2 4))) Cos[2 \[Pi] x]; (*Define your signal*)
tmp = Table[{\[CapitalDelta], \[Sigma], NIntegrate[signal*wavelet[(x - \[CapitalDelta])/\[Sigma]], {x, -20, 20}]}, {\[CapitalDelta], -6, 6, 0.05}, {\[Sigma], 0.1, 2.4, 0.2}]; (*Calculate the wavelet transform for a discrete set of shifts and stretchings*)
p1 = Table[
   Grid[{{
      Plot[{signal, wavelet[(x - tmp[[All, m]][[All, 1]][[l]])/tmp[[All, m]][[All, 2]][[1]]], signal*wavelet[(x - tmp[[All, m]][[All, 1]][[l]])/tmp[[All, m]][[All, 2]][[1]]]}, {x, -7, 7}, PlotRange -> All, 
       PlotStyle -> {Directive[Black], Directive[Red], Directive[Thin, Purple]}, Filling -> {3 -> Axis}, ImageSize -> Large, Ticks -> None, Axes -> {True, False}]
      ,
      Show[
       Table[
        ListPointPlot3D[If[n < m, tmp[[All, n]], tmp[[1 ;; l, n]]] , PlotRange -> {{-6, 6}, {0, 2.35}, {-0.7, 0.7}}, PlotStyle -> Directive[Black], Filling -> Bottom, FillingStyle -> Directive[White, Thickness[0.005] ], ViewPoint -> {1.3, 2.4, 2.}] /. Point[a___] :> {Thickness[0.015], Line[a]}
        , {n, 1, m}]
       , PlotLabel -> "\[Integral]s(x)*w(\!\(\*FractionBox[\(x - \[CapitalDelta]\), \(\[Sigma]\)]\)) dx", LabelStyle -> {Black, Bold, FontSize -> 18}, AxesLabel -> {"\[CapitalDelta]", "\[Sigma]", ""},        ImageSize -> Large ]
      }}]
   , {m, 1, Dimensions[tmp][[2]], 1}, {l, 1, Dimensions[tmp][[1]], 10}];
ListAnimate[Flatten[p1]]