4 ms·
Ok but when i try this, i dont get any good intuitions. polynomial multiplication is convolution, so what am i supposed to do here when you say, "g is blurring
by nh23423fefe 3y ago
Ok but when i try this, i dont get any good intuitions.
polynomial multiplication is convolution, so what am i supposed to do here when you say, "g is blurring function"
When i think of multiplying term by term an summing over the diagonal I can clearly see what the f(tau)g(t-tau) is doing, its collecting terms with like exponents.
This also makes sense when I think of probability distributions, i'm multiplying the densities and summing "over the diagonal"
- ndriscoll 3y agoIf you plot your coefficients as if they were a discrete time signal, you ought to see multiplication appear as a blur I guess, but yeah IMO it's hard to interpret for polynomials because polynomials are very abstract. I'd certainly look at the diagonal (or what I said is the "symmetric" way to write it) as the proof for "why" convolution appears in the sum of random variables, and I've never considered the blurring thing in that setting, but it actually makes a lot of intuitive sense for looking at "what" happens when you add distributions. Like just picturing repeated blurrings of a uniform distribution at the origin (i.e. start with a square and blur with a square over and over), it seems intuitively plausible that it will converge to something like a gaussian (i.e. that you'll get a bump of some kind), so that's neat.