Before revision:  We provide basic introductions to simplicial complexes and hypergraphs, making special emphasis on the concepts needed for processing signals on them. Leveraging these concepts , we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and non-linear processing through neural networks in these two representations of polyadic relational structures .
After revision:  We provide basic introductions to simplicial complexes and hypergraphs, making special emphasis on the concepts needed for the processing of signals supported on these structures. Specifically , we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and non-linear processing through neural networks in these two representations of polyadic relational structures .