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: