Abstract
The idea of Fourier analysis is to express general functions as sums of other choices of basic functions such as sines and cosines. One can interpret it as decomposing a vector into a set of basis vectors in the context of linear algebra. This paper will discuss differential equations and specifically focusing on approximating solutions using Fourier analysis. In modern times, Fourier analysis is not only used in the field of signal processing. As an important subfield of mathematical analysis, Fourier analysis has been broadly applied to various engineering fields, such as image processing, vibration analysis, acoustics, etc.
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