The Companion Model -- a Canonical Model in Graph Signal Processing

• DOI: 10.48550/arxiv.2203.13791
• Publication Date: 2022-01-01
• Authors: J. Y. Shi; José M. F. Moura
• Keywords: Convolution (computer science); Discrete-time signal

This paper introduces a $\textit{canonical}$ graph signal model defined by and shift, the $\textit{companion}$ shift. These are canonical because, under standard conditions, we show that any processing (GSP) can be transformed into model. The transform obtains this is $z$-transform ($\textrm{G$z$T}$) introduce. GSP comes closest to discrete (DSP) time models: structure of companion shift decomposes line continuation just like DSP directed with terminal condition reflecting condition. We further that, surprisingly, in model, convolution signals fast FFT.