A unified treatment of 1D signal convolution, 2D image convolution via the convolution theorem, and graph convolution as a spectral operation on the normalized Laplacian.

Applying Spectral GCNs to heat diffusion on a 3-D torus: the heat kernel filter, PyTorch implementation, Chebyshev approximation, and the cold-start connection.

How the classical Fourier Transform generalises to arbitrary graphs: deriving the Graph Fourier Transform from the Laplacian eigenbasis and building up to the one-layer Spectral GCN.

A drop-in Python implementation of MATLAB's resample function using scipy's polyphase filter — matching MATLAB's output exactly, with no signal-processing background required.