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

TL;DR

This paper introduces a novel graph linear canonical transform based on CM-CC-CM decomposition, offering reduced computational complexity and improved reversibility for graph signal processing applications.

Contribution

It proposes a new CM-CC-CM-GLCT that is sampling-period independent, computationally efficient, and compares favorably with existing transforms in properties.

Findings

Reduced computational complexity compared to existing methods

Achieves similar additivity to CDDHFs-GLCT

Exhibits better reversibility

Abstract

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.