title: Image 2x downsampling with Lanczos filter
body: <p>I'm trying to implement image downsampling with Lanczos2.</p>
  
  <p>However, the kernel seems to have zeros everywhere (since sin(pi*x)=0 if x is integer) <a href="http://www.realitypixels.com/turk/computergraphics/ResamplingFilters.pdf" rel="noreferrer">except at the center pixel</a>.</p>
  
  <p>Thus, if the downsampling factor is an integer number (e.g. the output size is 1/2 of the original size at each dimension), then the Lanczos downsampling yields the exact same result as nearest neighbor interpolation (just taking every other pixel in 2X downsampling).</p>
  
  <p>I believe that this is not intended to be the case, so my question is:
  What am I missing?</p>
  
  <p>How to use lanczos2 filter for 2x downsampling and is the result expected to be different than simply take every other pixel?</p>