| Summary: | 碩士 === 國立臺灣大學 === 電信工程學研究所 === 106 === Graph signal processing is a research area dealing with signals on graph, and Graph Fourier transform is a cornerstone of it. Different with discrete Fourier transform, who has fast Fourier transform as its fast implementation method, a full matrix-vector multi-plication is needed for a graph Fourier transform, which contains O(n^2) operations.
Nevertheless, when a graph has some special structure, their graph Fourier trans-form will have some properties similar to the fast Fourier transform. Thus can be accel-erated by factorization with sparse matrices. On the other hand, Luc Le Magoarou el. proposed a numeric approximation method for graph Fourier transform of general graphs by constructing sparse matrix using Givens rotation. By modifying their idea, we pro-posed a method which can approximate a graph Fourier transform by another one. At last, we found some approaches to detect whether a graph has or near to a special struc-ture. With all the methods mentioned, a new process to compute the decomposition of graph Fourier transform is obtained.
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