I don't understand why the first operations of a CNN are FFT-based decomposition into spatial wavelets. This is basically all the first layers are doing anyways

I don't understand why the first operations of a CNN are FFT-based decomposition into spatial wavelets. This is basically all the first layers are doing anyways. In fact the filters usually learn both an edge and a centroid at a given orientation. You can get both at the same time with complex wavelets.