Beyond Single-Window Graph Fourier Analysis
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915757469728768 |
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| author | Bulai, Iulia Martina Cordero, Elena Pucci, Edoardo Saliani, Sandra |
| author_facet | Bulai, Iulia Martina Cordero, Elena Pucci, Edoardo Saliani, Sandra |
| contents | We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework extends the windowed graph Fourier transform by allowing multiple analysis and synthesis windows. Exact reconstruction formulas are derived for complex-valued graph signals, together with sufficient and computable conditions guaranteeing stable invertibility. The associated families of windowed graph Fourier atoms are shown to form frames for the space of graph signals. Numerical experiments on synthetic and real world graphs confirm exact reconstruction up to machine precision and demonstrate improved stability and vertex-frequency localization compared to single-window constructions, particularly on irregular graph topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Single-Window Graph Fourier Analysis Bulai, Iulia Martina Cordero, Elena Pucci, Edoardo Saliani, Sandra Classical Analysis and ODEs Signal Processing We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework extends the windowed graph Fourier transform by allowing multiple analysis and synthesis windows. Exact reconstruction formulas are derived for complex-valued graph signals, together with sufficient and computable conditions guaranteeing stable invertibility. The associated families of windowed graph Fourier atoms are shown to form frames for the space of graph signals. Numerical experiments on synthetic and real world graphs confirm exact reconstruction up to machine precision and demonstrate improved stability and vertex-frequency localization compared to single-window constructions, particularly on irregular graph topologies. |
| title | Beyond Single-Window Graph Fourier Analysis |
| topic | Classical Analysis and ODEs Signal Processing |
| url | https://arxiv.org/abs/2601.19009 |