I have recently come across the idea of encoding a 1D signal (i.e. a mono audio) as a complex vector instead of as a vector of reals, where the imaginary part is used to encode the cells' positions. It can be further generalized to a way of encoding a grayscale image into a vector of quaternions where imaginary parts now encode the pixels' positions. Here is the link to the paper discussing this way of encoding: https://arxiv.org/pdf/2006.08321.pdf The paper further goes on to octonions to encode data higher than 3D and concludes with geometric algebra.
My question is on the implications of this kind of encoding for signal processing theory in general. Will this kind of encoding be useful in any application? Does it have any further implications?