It's a stretch to call it a neural network. It was already well-known that the Fourier transform can be seen as a matrix multiply which minimizes some least squ

It's a stretch to call it a neural network. It was already well-known that the Fourier transform can be seen as a matrix multiply which minimizes some least squares problem. This can be found somewhere in S.M. Kay's Fundamentals of Statistical Signal Processing: Estimation Theory (Vol 1), Detection Theory (Vol 2).