TY - GEN
T1 - The Fractional Fourier Transform on Graphs
T2 - 8th International Conference on Signal and Image Processing, ICSIP 2023
AU - Zhang, Yu
AU - Li, Bing Zhao
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - The fractional Fourier transform on graph (GFrFT) is an extension of discrete fractional Fourier transform (DFrFT) based on graph signal processing (GSP). In this paper, we discuss the shift, polynomial filters, delta functions, the convolution and modulation of graph signal in fractional domain. First, we review the basic theory of discrete graph signal processing, concepts of graph signals and GFrFT. Then, similar to the definition of the shift of adjacency matrix in vertex domain, the shift matrix of graph spectral domain in the GFrFT is defined. Finally, the new polynomial filters are used to illustrate the convolution and modulation of fractional graph signals in the vertex domain and graph spectral domain, and the relationship between the delta functions and convolution is discussed.
AB - The fractional Fourier transform on graph (GFrFT) is an extension of discrete fractional Fourier transform (DFrFT) based on graph signal processing (GSP). In this paper, we discuss the shift, polynomial filters, delta functions, the convolution and modulation of graph signal in fractional domain. First, we review the basic theory of discrete graph signal processing, concepts of graph signals and GFrFT. Then, similar to the definition of the shift of adjacency matrix in vertex domain, the shift matrix of graph spectral domain in the GFrFT is defined. Finally, the new polynomial filters are used to illustrate the convolution and modulation of fractional graph signals in the vertex domain and graph spectral domain, and the relationship between the delta functions and convolution is discussed.
KW - Graph signal processing
KW - convolution
KW - fractional Fourier transform on graph
KW - modulation
UR - https://www.scopus.com/pages/publications/85174686007
U2 - 10.1109/ICSIP57908.2023.10271073
DO - 10.1109/ICSIP57908.2023.10271073
M3 - Conference contribution
AN - SCOPUS:85174686007
T3 - 2023 8th International Conference on Signal and Image Processing, ICSIP 2023
SP - 737
EP - 741
BT - 2023 8th International Conference on Signal and Image Processing, ICSIP 2023
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 8 July 2023 through 10 July 2023
ER -