Discrete Fourier Transform with Neural Networks

The discrete Fourier transform is an important computational tool to retrieve the frequency distribution of a sampled signal. Recent years have also witnessed considerable research activity in neural networks as a mean to solve various signal processing problems. Despite this, it has been an open issue whether a neural network can be trained to return the discrete Fourier transform of its inputs. This paper presents a training methodology for neural networks with non-linear activation functions to replicate and approximate the discrete Fourier transform.