Spectral Projector-Based Graph Fourier Transforms

@article{Deri2017SpectralPG,
  title={Spectral Projector-Based Graph Fourier Transforms},
  author={Joya A. Deri and Jos{\'e} M. F. Moura},
  journal={IEEE Journal of Selected Topics in Signal Processing},
  year={2017},
  volume={11},
  pages={785-795}
}
This paper considers the definition of the graph Fourier transform (GFT) and of the spectral decomposition of graph signals. Current literature does not address the lack of unicity of the GFT. The GFT is the mapping from the signal set into its representation by a direct sum of irreducible shift invariant subspaces: 1) this decomposition may not be unique; and 2) there is freedom in the choice of basis for each component subspace. These issues are particularly relevant when the graph shift has… 

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