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.
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: