To see how the Fourier coefficients, a_{i} and b_{i},
influence a given harmonic component, use the applet below to vary the
a_{1} and b_{1} 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) = a_{0} + a_{1}cos(x) + b_{1}sin(x)
+
a_{2}cos(2x) + b_{2}sin(2x) + a_{3}cos(3x) + b_{3}sin(3x) + ... a_{n}cos(nx) + b_{n}sin(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 |
To change the value of a Fourier coefficient:
** 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.
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
Please e-mail kewley@indiana.edu with questions, comments, or problems related to this site.