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 hardware applet can be viewed at the Institut für Netzwerktheorie und Schaltungstechnik, TU Braunschweig.

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

• Enhanced version from Tom Huber, huber@gac.edu

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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