## Fourier Synthesis

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.

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

The source code (version 2000/03/25) is available according to the GNU Public License.

**Other Versions of this Applet:**

**Condition of Dirichlet:**

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.

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Manfred Thole,
manfred@thole.org
Last modified: Sat Jan 24 23:48:02 MET 2004