Fourier Applet

IV. Test of Fourier Coefficients

To see how the Fourier coefficients, a_i and b_i, influence a given harmonic component, use the applet below to vary the a₁ and b₁ values independently. Set all other coefficients to zero so that you can see the influence a and b have on the starting phase of harmonic 1. Then use the applet to create interesting stimuli such as a sawtooth wave, a square wave, and a triangle wave (recall that the "recipies" for these waveforms were given in the reading material for Lecture 11).

f(x) = a₀ + a₁cos(x) + b₁sin(x) +
                 a₂cos(2x) + b₂sin(2x) +
                 a₃cos(3x) + b₃sin(3x) + ...
                 a_ncos(nx) + b_nsin(nx) Fourier's theorem states that any complex stimulus, f(x), can be represented as a sum of sinusoidal components. Note that: 1) the coeffients a_i and b_i are scalar values; 2) the right hand side of the equation is an harmonic series; and 3) while cosine and sine are orthogonal, their sum uniquely determines the amplitude and starting phase of each harmonic in the series.

APPLET
INSTRUCTIONS	ACKNOWLEDGEMENTS

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APPLET INSTRUCTIONS:

To change the value of a Fourier coefficient:

Reposition the sliding bar next to a given coefficient.
Use the arrows to the left and right of the sliding bar.

To "zero out" or turn off a particular coefficient:

Click on the coefficient label (e.g., a1).
Reposition the sliding bar so that the value in the center reads 0.00

Choose "Audio On" or Audio Off" to turn on or off the sound output.

** The formula bars above the cosine and sine coefficients and the Wave 1, Wave 2, Wave 3 storage capabilities are not active at this time.

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APPLET ACKNOWLEDGEMENTS:

This applet was originally 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, as found at http://www.gac.edu/~huber/fourier/. This site contains the source code for these modifications (version 96/09/27), which is available according to the GNU Public License.

This applet requires the graph2d package from Leigh Brookshaw to parse equations, which can be downloaded from http://www.sci.usq.edu.au/staff/leighb/graph

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Please e-mail kewley@indiana.edu with questions, comments, or problems related to this site.