Graph Signal Processing: Modulation, Convolution, and Sampling

• DOI: 10.48550/arxiv.1912.06762
• Publication Date: 2019-01-01
• Authors: J. Y. Shi; José M. F. Moura
• Keywords: Signal Processing (eess.SP); 0202 electrical engineering, electronic engineering, information engineering; FOS: Electrical engineering, electronic engineering, information engineering; 02 engineering and technology; Electrical Engineering and Systems Science - Signal Processing

To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) redefining traditional concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation, convolution, sampling of graph signals as appropriate natural extensions the corresponding concepts. define these for both vertex frequency domains, we associate with generic G its shift A, a spectral M Gs. leads GSP theory that parallels in domain existing domain. The applies this design recovery techniques directed graphs.