Graph Linear Canonical Transform Based on CM-CC-CM Decomposition

Fuente: arXiv
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Main Authors: Li, Na, Zhang, Zhichao, Han, Jie, Chen, Yunjie, Cao, Chunzheng
Format: Preprint
Published: 2024
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_version_ 1866910541303250944
author Li, Na
Zhang, Zhichao
Han, Jie
Chen, Yunjie
Cao, Chunzheng
author_facet Li, Na
Zhang, Zhichao
Han, Jie
Chen, Yunjie
Cao, Chunzheng
contents The graph linear canonical transform (GLCT) is presented as an extension of the graph Fourier transform (GFT) and the graph fractional Fourier transform (GFrFT), offering more flexibility as an effective tool for graph signal processing. In this paper, we introduce a GLCT based on chirp multiplication-chirp convolution-chirp multiplication decomposition (CM-CC-CM-GLCT), which irrelevant to sampling periods and without oversampling operation. Various properties and special cases of the CM-CC-CM-GLCT are derived and discussed. In terms of computational complexity, additivity, and reversibility, we compare the CM-CC-CM-GLCT and the GLCT based on the central discrete dilated Hermite function (CDDHFs-GLCT). Theoretical analysis demonstrates that the computational complexity of the CM-CC-CM-GLCT is significantly reduced. Simulation results indicate that the CM-CC-CM-GLCT achieves similar additivity to the CDDHFs-GLCT. Notably, the CM-CC-CM-GLCT exhibits better reversibility.
format Preprint
id arxiv_https___arxiv_org_abs_2407_17513
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Graph Linear Canonical Transform Based on CM-CC-CM Decomposition
Li, Na
Zhang, Zhichao
Han, Jie
Chen, Yunjie
Cao, Chunzheng
Information Theory
Signal Processing
The graph linear canonical transform (GLCT) is presented as an extension of the graph Fourier transform (GFT) and the graph fractional Fourier transform (GFrFT), offering more flexibility as an effective tool for graph signal processing. In this paper, we introduce a GLCT based on chirp multiplication-chirp convolution-chirp multiplication decomposition (CM-CC-CM-GLCT), which irrelevant to sampling periods and without oversampling operation. Various properties and special cases of the CM-CC-CM-GLCT are derived and discussed. In terms of computational complexity, additivity, and reversibility, we compare the CM-CC-CM-GLCT and the GLCT based on the central discrete dilated Hermite function (CDDHFs-GLCT). Theoretical analysis demonstrates that the computational complexity of the CM-CC-CM-GLCT is significantly reduced. Simulation results indicate that the CM-CC-CM-GLCT achieves similar additivity to the CDDHFs-GLCT. Notably, the CM-CC-CM-GLCT exhibits better reversibility.
title Graph Linear Canonical Transform Based on CM-CC-CM Decomposition
topic Information Theory
Signal Processing
url https://arxiv.org/abs/2407.17513