Optimal filters

https://dsp.stackexchange.com/questions/9745/which-iir-filters-approximate-a-gaussian-filter

Gaussian blur can be approximated by a (fixed size) IIR filter:

https://www.intel.com/content/dam/develop/external/us/en/documents/gaussian-filter-181134.pdf

FIR are polynomials and IIR are rational functions:

https://en.wikipedia.org/wiki/Infinite_impulse_response

Remco Bloemen
Math & Engineering
https://2π.com