Rectangular Fourier transform

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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?

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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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0xDEADBEEF	Rectangular Fourier transform Tweet 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?