I'll leave these here: https://en.wikipedia.org/wiki/Multiresolution_analysis https://en.wikipedia.org/wiki/Discrete_wavelet_transform

And as a lot of people have mentioned in here, DFT is pretty much implicated in neural networks already because of the mathematics (especially in convolutional/correlational neural networks, which often make use of the convolution theorem (which is "just" fourier coefficient multiplication) to do the convolution)

Extending this post it seems more interesting to look more generally at the correspondence with wavelet-transforms.