# Rectangular Fourier transform

1. Oct 26, 2012

Is there a name for a transformation using the orthonormal base

$$s_k(x)=\lceil \sin kx \rceil,\: c_k(x) = \lceil \cos kx \rceil \quad ?$$

So basically a Fourier transform or Fourier series using periodic rectangles. What are the properties? Is there some kind of convolution theorem?

2. Oct 27, 2012