由图形短时傅立叶变换生成的紧帧

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-11-19 DOI:10.1016/j.laa.2024.11.014

Martin Buck, Kasso A. Okoudjou

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引用次数: 0

摘要

我们利用图拉普拉卡的特征向量和图热核定义了图短时傅立叶变换，并将其作为由非负时间参数 t 参数化的窗口。我们证明了相应的类 Gabor 系统形成了 Cd 的框架，并用图热核和底层图拉普拉卡的频谱描述了相应框架算子的频谱。对于两类代数图，我们证明了框架是紧密的，且与窗口参数 t 无关。

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Tight frames generated by a graph short-time Fourier transform

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 nonnegative time parameter t. We show that the corresponding Gabor-like system forms a frame for

C^{d}

and gives 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.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.