A periodic signal can be described by a Fourier decomposition as a Fourier series, i. e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves. The general function is:

The Fourier series of a square wave is

or

The Fourier series of a saw-toothed wave is

The approximation improves as more oscillations are added.

A sample session would be as follows:

- To produce a saw-toothed wave,
in the white box to the right of the word "Sin:" enter a
formula such as
`1/x`

or`(-1^(x-1))/x`

. The variable`"x"`

will be replaced by the term number, so the coefficients will have values of 1, 0.5, 0.3333,... - IN ORDER FOR THE PROGRAM TO PARSE AN EXPRESSION, you must press the "Enter" key instead of leaving the box with the mouse or cursor keys.
- You can modify coefficients by using the formula box, the slider bars, or by entering an expression (such as 0.5 or -1/7) into the white box by each label.
- If your machine is capable of playing sounds, you should also hear a tone for the waveform you have produced. This may be turned off by pressing the "Audio Off" button.
- You may reset a coefficient to zero by clicking on the label button
with the mouse, thus by clicking on the even numbered coefficients
`b2:`

,`b4:`

, ..., you can produce a square wave. - The applet can store up to 3 different waveforms (by clicking on Wave1, Wave2, Wave3) which is helpful for comparing different sequences or different numbers of terms.

The Fourier series of a periodic function x(t) exists, if

- , i. e. x(t) is absolutely integratable,
- variations of x(t) are limited in every finite time interval T and
- there is only a finite set of discontinuities in T.

View this page in Romanian courtesy of azoft

The source code (version 96/09/27) is available according to the GNU Public License

This applet uses the sun.audio package. HotJava users should set
`Class access` to `Unrestricted`.

This applet, gif images and HTML documentation were developed by Manfred Thole, thole@nst.ing.tu-bs.de, July 15, 1996. The original documentation and applets can be found at:

Deutsch http://www.nst.ing.tu-bs.de/schaukasten/fourier/

English http://www.nst.ing.tu-bs.de/schaukasten/fourier/en_idx.html

Modifications were made by Tom Huber, huber@gac.edu, September 27, 1996

This applet requires the graph2d package from Leigh Brookshaw to parse equations.

Tom Huber, huber@gac.edu, Revised 24-Aug-2008

Since August 24, 2008, You Are Visitor Number :