DefinitionThe Fourier series is a method to represent a periodic function as the sum of simple sine waves. First, I would like to say that a Fourier series is a technique by which a periodic function may be broken down into a sum of simple functions, in which each term represents a different frequency of wave (frequency=1/time period of wave) and has frequency content is how much of that frequency is there in the function. The Fourier series coefficients tell us “how much” of each harmonic to include in our function. In signal processing and related fields, a Fourier series is a way to represent a function as the sum of simple sine waves. For example: f(x)=2a0+∑n=1∞(ancos(nx)+bnsin(nx)) will be the Fourier series representation of a periodic function f(x) with period 2π where a0, an, and bn are Fourier coefficients.
