A survey of convolution

Abstract

Convolution is a mathematical method of integral transformation and an important operation in analytical mathematics. The concept of convolution can also be extended to sequence, measure and generalized functions. Convolution has many applications in mathematics and engineering. For example, it can be widely used as a linear operation in image filtering, digital signal processing, electronic engineering and other application scenarios such as fluid mechanics, statistics, physics, astronomy, thermodynamics, optics. It plays a very key role in such important disciplines as it is a very common tool to help people solve problems. This paper gives a more detailed description of continuous convolution, discrete convolution and two-dimensional convolution through formula method and definition method, and points out their common application fields, and then discusses discrete convolution and continuous convolution through common scenes in life which is the simple explanation. The deep application of convolution in the signal field and Fourier transform field is sorted out. Finally, combining with the background of the era of big data, the multi-faceted applications of the future convolutional network neural field are discussed.