To define the continuous wavelet transform in Mathematica, you need Fourier factor and Fourier transform. I don't understand how to find these two, for example, how can define these two in the haar wavelet transform:

f[x_] := Piecewise[{{1, 0 <= x <= 1}}]
g[x_] := f[2 x] - f[2 x - 1])

and these two are defined for f[x_] or g[x_]?

  • $\begingroup$ Is it not a duplication of mathematica.stackexchange.com/questions/108963/… ? $\endgroup$
    – user64494
    Oct 12, 2023 at 9:55
  • $\begingroup$ I saw the page you mentioned, but I don't understand how it defines Fourier transform and Fourier factor so that I can define these two for continuous wavelet transform, for example Morlet or shannon. $\endgroup$ Oct 14, 2023 at 11:02


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