Convolutional Neural Networks from the Perspective of Fourier Transform

The learned convolution operation process of convolutional neural networks (CNNs) can be understood as a Fourier transform, or Fourier series expansion. Essentially, this means it is the weighted sum of different orthogonal vectors. The convolution kernel can be seen as understanding the dimensional orthogonal vector. This perspective is not only insightful for grasping the essence of CNNs but can also be further helpful to understand the position coding of transformers. At the same time, CNNs have the potential to be combined with signal processing techniques. This combination can improve the traditional signal transmission mode to a certain extent by providing more efficient and robust methods for signal analysis and processing. This paper will explain the basic principles of CNNs from this new perspective. It aims to help people see why CNNs can be effectively applied in the field of signal transmission, offering a fresh understanding of their capabilities and potential applications in this area.