# Constructing Dampened LTI Systems Generating Polynomial Bases

arXiv: https://arxiv.org/abs/2103.00051 · HTML: https://mlsanity.com/paper/2103.00051/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 9 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 1 of 1)

- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)

## Built on by (most cited first, 1 of 1)

- [Discrete Function Bases and Convolutional Neural Networks](https://mlsanity.com/paper/2103.05609/) (2021)

## Abstract (arXiv)

We present an alternative derivation of the LTI system underlying the Legendre Delay Network (LDN). To this end, we first construct an LTI system that generates the Legendre polynomials. We then dampen the system by approximating a windowed impulse response, using what we call a "delay re-encoder". The resulting LTI system is equivalent to the LDN system. This technique can be applied to arbitrary polynomial bases, although there typically is no closed-form equation that describes the state-transition matrix.