The following paper is excellent and not totally irrelevant:<p><a href="http://home.agh.edu.pl/~turcza/sr/Splitting%20the%20Unit%20Delay.pdf" rel="nofollow">http://home.agh.edu.pl/~turcza/sr/Splitting%20the%20Unit%20D...</a><p>The effects you're describing (blurring, numerical stability) are readily formalized in DSP jargon. It's a shame this post didn't provoke more discussion here.