Print Email Facebook Twitter Finite Impulse Response Filters for Simplicial Complexes Title Finite Impulse Response Filters for Simplicial Complexes Author Yang, Maosheng (TU Delft Multimedia Computing) Isufi, E. (TU Delft Multimedia Computing) Schaub, Michael T. (Rheinisch-Westfälische Technische Hochschule) Leus, G.J.T. (TU Delft Signal Processing Systems) Date 2021 Abstract In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Specifically, we discuss how, unlike in the case of node signals, the Fourier transform in the context of edge signals can be understood in terms of two orthogonal subspaces corresponding to the gradient-flow signals and curl-flow signals arising from the Hodge decomposition. By assigning different filter coefficients to the associated terms of the Hodge Laplacian, we develop a subspace-varying filter which enables more nuanced control over these signal types. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation. Subject Hodge decompositionHodge Laplaciansimplicial complexessimplicial filtersTopological signal processing To reference this document use: http://resolver.tudelft.nl/uuid:87315d6c-4be2-4f08-98ca-5f6c98b08188 DOI https://doi.org/10.23919/EUSIPCO54536.2021.9616185 Publisher IEEE Embargo date 2022-06-08 ISBN 978-1-6654-0900-1 Source 2021 29th European Signal Processing Conference (EUSIPCO): Proceedings Event 2021 29th European Signal Processing Conference (EUSIPCO), 2021-08-23 → 2021-08-27, Virtual at Dublin, Ireland Bibliographical note Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type conference paper Rights © 2021 Maosheng Yang, E. Isufi, Michael T. Schaub, G.J.T. Leus Files PDF Finite_Impulse_Response_F ... plexes.pdf 554.38 KB Close viewer /islandora/object/uuid:87315d6c-4be2-4f08-98ca-5f6c98b08188/datastream/OBJ/view