Representing Fourier Transforms and Advanced Signal Processing as Convolutional Neural Networks

We present novel techniques for representing signal processing operations such as frequency-domain transforms, spectrogram generation and MFCC extraction as neural networks. In many applications, signal processing operations are performed in a separate step before a neural network (i.e. data preprocessing) or as a layer inside the neural network itself. Examples of such applications include radar, audio and medical imaging, all of which typically involve Fourier analysis. In such applications, it is often advantageous to represent signal processing operations in terms of common neural network layers, such as convolutions, elementwise and split/concatenate operations. By representing signal processing operations as neural networks, it is possible to execute them as part of a neural network.