# Multi-dimensional graph fractional Fourier transform and its application

arXiv: https://arxiv.org/abs/2109.04358 · HTML: https://mlsanity.com/paper/2109.04358/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2021.

## Built on by (most cited first, 3 of 3)

- [Graph Embedding in the Graph Fractional Fourier Transform Domain](https://mlsanity.com/paper/2508.02383/) (2025)
- [A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application](https://mlsanity.com/paper/2508.16633/) (2025)
- [Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering](https://mlsanity.com/paper/2511.16111/) (2025)

## Abstract (arXiv)

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of graph signal processing. This paper investigates the novel transform for multi-dimensional signals defined on Cartesian product graph and studies several related properties. Our work includes: (i) defining the multi-dimensional graph fractional Fourier transform (MGFRFT) based on Laplacian matrix and adjacency matrix; (ii) exploring the advantages of MGFRFT in processing multi-dimensional signals in terms of spectrum and computational time; (iii) applying the proposed transform to data compression to highlight the utility and effectiveness of it.