(1) Fourier expansion Fourier expansion is to rewrite a periodic function into the sum of a series of sine functions and cosine functions, and the limit of this sum is equal to the original function. Although sine and cosine are only 90 degrees apart, they are easy to understand and will be mentioned later. Each coefficient of the series is called "Fourier coefficient" and can be recorded as F(nw). W is the angular frequency (fundamental frequency) corresponding to the period of the original function.

(2) For aperiodic functions, Fourier transform needs to be generalized if it wants to be "expanded" like (1). This problem can be solved by expanding the original "sum of discrete series" to "sum of continuous integers" (please refer to the textbook for specific derivation. The expression of this continuous integral sum is called "inverse Fourier transform". In the inverse transformation, the original F(nw) is extended to f (w); Its value is the limit of 2PI*F(nw)/w, where w tends to zero. Here, w and w are used to distinguish two independent variables, where dW = delta(nw). Obviously, the expression of F(W) can be solved by the inverse Fourier transform equation. This is the "Fourier transform".