Fourier Transform in Three Differences Spaces

This paper starts by introducing the application of the Fourier analysis and divides the Fourier analysis into four cases according to the difference between physical space and frequency space: discrete points on a circle discrete points on a circle, , , and . The four cases are then grouped into three parts: the discrete Fourier transform (DFT), the Fourier series, and the Fourier transform. For each part, this paper discusses its characteristics and basic theory, and selectively deals with the proof and application examples. This paper will promote some research related to Fourier analysis by analyzing Fourier analysis in three different spaces as a whole.