Fourier series
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A Fourier series represents a periodic function as a sum of sine and cosine waves, or equivalently as a sum of complex exponentials. Each component has a frequency that is an integer multiple of a fundamental frequency.
The coefficients measure the amplitude and phase of each harmonic. They are calculated by integrating the function against the corresponding sine, cosine, or exponential basis functions over one period.
Under suitable conditions, the series converges to the original function. Near a jump discontinuity, partial sums show the persistent overshoot known as the Gibbs phenomenon.
Fourier series are used in heat transfer, acoustics, signal processing, vibration analysis, electrical engineering, image compression, quantum mechanics, and the solution of differential equations.
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- Source / publisher: Wikipedia
- URL type: WWW
- Credits: Wikipedia
- URL: https://en.wikipedia.org/wiki/Fourier_series