title: How to compute the derivative of a function through the Fourier domain?
body: <p>I am currently working on a project where I have to reconstruct an Image from its gradient by solving a Poisson equation, which we solve in the Fourier domain.</p>
  
  <p>The solution involves the product of the image's FT and that of the discrete derivation filter. In the Fourier domain, this is defined as the coordinate-wise product of the two.</p>
  
  <p>I understand how the FT of an image is computed, however I have trouble understanding how I should compute that of a filter, as <code>[0 -1 1]</code> for horizontal differences. Should I use the same formula as for images? This seems weird to me as I would keep only 2 components of my FT after having multiplied it with the image's FT.</p>