# Discrete Signal Processing on Meet/Join Lattices

arXiv: https://arxiv.org/abs/2012.04358 · HTML: https://mlsanity.com/paper/2012.04358/

## Key facts

- Cited by 8 papers in the map (data through 13 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 8 of 8)

- [Causal Fourier Analysis on Directed Acyclic Graphs and Posets](https://mlsanity.com/paper/2209.07970/) (2022)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)
- [Learning with Multigraph Convolutional Filters](https://mlsanity.com/paper/2210.16272/) (2022)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains including social data analysis, natural language processing, computational chemistry and biology, and database theory. In this paper we introduce discrete-lattice signal processing (DLSP), an SP framework for data, or signals, indexed by such lattices. We use the meet (or join) to define a shift operation and derive associated notions of filtering, Fourier basis and transform, and frequency response. We show that the spectrum of a lattice signal inherits the lattice structure of the signal domain and derive a sampling theorem. Finally, we show two prototypical applications: spectral analysis of formal concept lattices in social science and sampling and Wiener filtering of multiset lattices in combinatorial auctions. Formal concept lattices are a compressed representation of relations between objects and attributes. Since relations are equivalent to bipartite graphs and hypergraphs, DLSP offers a form of Fourier analysis for these structures.