Fourier Series Formula

About Fourier Series Formula

A periodic function f(x) is expanded in terms of an infinite sum of sines and cosines using the Fourier series formula. Any periodic function or periodic signal can be decomposed into the sum of a collection of simple oscillating functions, such as sines and cosines. Let's look at some examples of the Fourier series formula.

What Are Fourier Series Formulas?
The orthogonal relationships of the cosine and sine functions are used in the Fourier series. A function's Fourier series formula is as follows:

f(x) = 12a0 + ∑n-1∞ an cos nx + ∑n-1∞ bn sin nx

 

 where,
  • a0 = 1π∫-ππ f(x)dx
  • an = 1π∫-ππ f(x) cos nx dx
  • bn = 1π∫-ππ f(x) sin nx dx
  • n = 1, 2, 3.....

 

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Fourier Series Formula

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