https://github.com/pvdberg1998/maxpol
Exact solutions to the MaxPol kernel
https://github.com/pvdberg1998/maxpol
exact mathematica maxpol
Last synced: 3 months ago
JSON representation
Exact solutions to the MaxPol kernel
- Host: GitHub
- URL: https://github.com/pvdberg1998/maxpol
- Owner: PvdBerg1998
- License: gpl-3.0
- Created: 2022-01-03T16:17:33.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2022-01-12T14:39:03.000Z (almost 4 years ago)
- Last Synced: 2025-07-30T20:12:42.993Z (5 months ago)
- Topics: exact, mathematica, maxpol
- Language: Mathematica
- Homepage:
- Size: 17.2 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# MaxPol
MaxPol is a lowpass derivative kernel optimized to have "ideal" spectral properties. See literature: https://arxiv.org/abs/1709.08321, https://ieeexplore.ieee.org/document/7944698 for more details. Unfortunately there is no closed form for the kernel with general parameters. I present analytical (exact) solutions for the centralized MaxPol kernel, with `s=0` (no shift). Implements the same algorithm as the original [solver](https://github.com/mahdihosseini/MaxPol), but in Mathematica instead of Matlab. Shifting can be implemented trivially if required.
## This repository
This repository contains the solutions for `n=0..4`, `l=1..100` (i.e. zero'th to fourth derivatives with a filter length up to 201) and all possible `P,Q` values (degree of lowpass filtering vs. tangency to exact derivative). The `n=0` setting corresponds to filtering only.
[maxpol_calc](/maxpol_calc.tar.gz) contains numerical values, truncated at 18 significant digits (more than `f64` precision). Each value is printed on a newline, starting from the leftmost filter coefficient. Each solution is named `maxpol_n_l_P
`.
[maxpol_calc_exact](/maxpol_calc_exact.tar.gz) contains all the exact fractions formatted in the same way.
It is recommended to make use of an intermediate storage format, such as the Sled database as implemented in [maxpol_rust](/maxpol_rust).
The approximate maxima of the spectra are stored in [maxpol_calc_cutoff](/maxpol_calc_cutoff.tar.gz), to be used as an indication of the cutoff frequency.
## License
Everything is released under the GPL-3.0 license. If you use my work in academic context, a citation would be appreciated:
```latex
@misc{maxpol_pvdb,
author = {Pim van den Berg},
title = {MaxPol analytical solutions up to l=100},
howpublished = {https://github.com/PvdBerg1998/MaxPol/}
year = {2022}
}
```