IV.  Test of Fourier Coefficients

To see how the Fourier coefficients, ai and bi, 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) + ...                   ancos(nx) + bnsin(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 ai and bi 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.

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:

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

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