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Rectangular Fourier transform

  1. Oct 26, 2012 #1
    Is there a name for a transformation using the orthonormal base

    [tex]s_k(x)=\lceil \sin kx \rceil,\: c_k(x) = \lceil \cos kx \rceil \quad ?[/tex]

    So basically a Fourier transform or Fourier series using periodic rectangles. What are the properties? Is there some kind of convolution theorem?
  2. jcsd
  3. Oct 27, 2012 #2
    I found some answers. The Walsh-transform looks very similar. I noticed that the functions are not orthogonal so sign(sin(kx)) and sign(cos(kx)) is probably a better choice.
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