Abstract
In this paper, we employ a graph signal processing approach to redefine Fourier-like number-theoretic transforms, which includes the Fourier number transform itself, the Hartley number transform and specific types of the cosine number transform and the sine number transform. Our strategy basically consists in identifying graphs whose Laplacian or adjacency matrix has an eigenbasis coinciding with the basis employed to define each of the aforementioned transforms. We then demonstrate how to extend this idea to multidimensional cases and provide a general definition, which corresponds to the graph Fourier number transform (GFNT). We develop illustrative examples and perform a preliminary investigation regarding the use of the GFNT in an image encryption scenario.
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