<p>The Fourier Transform relies on its kernels being defined with extreme precision at each point, float32, 64, and beyond, which makes most NNs, which are approximators, horrible candidates. It's also not exactly productive to learn what's already been perfected, unless for some feature extraction study.</p>
<p>The FT kernel <em>has</em>, however, been utilized as a mechanism, just like activation functions, in <a href="https://arxiv.org/abs/2010.08895" rel="nofollow noreferrer">Fourier Neural Operator for Parametric Partial Differential Equations</a>, with promising results:</p>
<p><a href="https://i.stack.imgur.com/XJFbB.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/XJFbB.png" alt="enter image description here" /></a></p>
<p>Regardless, such a design question is better suited for <a href="https://datascience.stackexchange.com/">Data Science</a> or <a href="https://ai.stackexchange.com/">AI</a> networks, and try being more specific with what you seek to accomplish.</p>
Can Neural Networks learn to do Fourier Transform?
<p>If I want to make a neural net that can compute the Fourier Transform of any input signal, what should be the architecture, dataset, loss function, etc.</p>
<p>My way would be, making a normal fully connected NN that takes as input a signal (array vector of some size) and outputs the fourier transform (same size vector), the loss function might be a coef. error that measures how far it is from the actual fourier transform (maybe dynamic time warping).
any suggestions would be appreciated.</p>