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.

No Java, no applet! Sorry! But it would look like this:

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

The source code (version 96/07/15) is available according to the GNU Public License.

Tom Huber, huber@gac.edu has written an enhanced version.

Condition of Dirichlet:
The Fourier series of a periodic function x(t) exists, if
1. , i. e. x(t) is absolutely integratable,
2. variations of x(t) are limited in every finite time interval T and
3. there is only a finite set of discontinuities in T.

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aktualisiert: 13.10.2010

Verantwortlich: Michael Hinz
Feedback an: m.hinz@tu-braunschweig.de