Graph Signal Processing: Modulation, Convolution, and Sampling
arXiv:1912.06762
Abstract
To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation, convolution, and sampling of graph signals as appropriate natural extensions of the corresponding DSP concepts. To define these for both the vertex and the graph frequency domains, we associate with generic data graph G and its graph shift A, a graph spectral shift M and a spectral graph Gs. This leads to a spectral GSP theory that parallels in the graph frequency domain the existing GSP theory in the vertex domain. The paper applies this to design and recovery sampling techniques for data supported by arbitrary directed graphs.
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Cited by in corpus (5)
- Graph Signal Processing and Deep Learning: Convolution, Pooling, and Topology
- Graph Fourier Transform: A Stable Approximation
- Graph Signal Sampling Under Stochastic Priors
- Graph Signal Processing: Dualizing GSP Sampling in the Vertex and Spectral Domains
- From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation