Fourier Series of Simple Functions

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The Fourier series approximations of five different periodic functions are presented together with the corresponding functions themselves. The convergence of the Fourier series (or lack thereof) can be tested by increasing the number of terms in the series. It should be noted that for continuous functions (such as the periodic extension of the parabola), a few terms in the Fourier series provide an excellent approximation. Continuous functions with continuous derivatives (such as the periodic extension of the cubic) can be well approximated with as few as two or three terms.
Contributed by: Alain Goriely (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
detailSectionParagraphPermanent Citation
"Fourier Series of Simple Functions"
http://demonstrations.wolfram.com/FourierSeriesOfSimpleFunctions/
Wolfram Demonstrations Project
Published: March 7 2011