Stephan Paukner :: syslog

(Q26) Meanwhile, I know that a convolution of one function with another function means that will be “-smeared”, and vice versa. I visualized some convolutions using Octave. I was prepared to implement for two vectors, but then stepped over HGFei’s conv2fei which makes the surprising use of the identity ; I wouldn’t have come to the idea to do it this way, you only have to multiply two FFT’s and then do the inverse FFT.

First I convolved a square with a small Gaussian—this is nothing less than a Gaussian blur:

Note that the blur would already occur even if the second object were solid! Look at the square convolved with itself:

Then I watched how these bars convolve with each other:

Notice how the blurness shrinks when the two objects can’t overlap much.

66. What are Fourier multipliers?
67. What are Frechet spaces? Why are and not Banach, but only Frechet?
68. Is there a difference between and in HGFei’s notation?
69. Why is ? (There’s a relation to Q2.)