Tight Frames Generated By A Graph Short-Time Fourier Transform
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917597328441344 |
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| author | Buck, Martin Okoudjou, Kasso |
| author_facet | Buck, Martin Okoudjou, Kasso |
| contents | A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a non-negative time parameter $t$. We show that the corresponding Gabor-like system forms a frame for $\mathbb{C}^d$ and give a description of the spectrum of the corresponding frame operator in terms of the graph heat kernel and the spectrum of the underlying graph Laplacian. For two classes of algebraic graphs, we prove the frame is tight and independent of the window parameter $t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tight Frames Generated By A Graph Short-Time Fourier Transform Buck, Martin Okoudjou, Kasso Spectral Theory Signal Processing Primary 42C15 Secondary 94A12 A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a non-negative time parameter $t$. We show that the corresponding Gabor-like system forms a frame for $\mathbb{C}^d$ and give a description of the spectrum of the corresponding frame operator in terms of the graph heat kernel and the spectrum of the underlying graph Laplacian. For two classes of algebraic graphs, we prove the frame is tight and independent of the window parameter $t$. |
| title | Tight Frames Generated By A Graph Short-Time Fourier Transform |
| topic | Spectral Theory Signal Processing Primary 42C15 Secondary 94A12 |
| url | https://arxiv.org/abs/2402.15902 |