MathLiveFourier series
Expresses a periodic function as an infinite sum of cosine and sine waves with frequencies that are whole-number multiples of the fundamental. It is used to analyse and approximate periodic signals and solutions of differential equations.
f(x) = \frac{1}{2} a_0 + \sum_{n=1}^{\infty} \left(a_n \cos(n x) + b_n \sin(n x)\right)What the symbols mean
| the periodic function being represented (with period 2\pi) | |
| independent variable | |
| constant (average) term of the series, twice the mean value of f | |
| Fourier cosine coefficient of the n-th harmonic | |
| Fourier sine coefficient of the n-th harmonic | |
| harmonic index, a positive integer |
About this formula
- FieldMathematics
- TopicFourier analysis
- LevelUniversity
- Also calledFourier series expansion, trigonometric series of a periodic function, sine and cosine series, Fourier series formula, decomposition of periodic function into sinusoids, Fourier expansion
- SourceWikidata Q179467
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