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.|
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.
RETURN TO APPLET
This applet was originally developed by Manfred Thole, email@example.com, July 15, 1996. The original documentation and applets can be found at:
Modifications were made by Tom Huber, firstname.lastname@example.org, 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
RETURN TO APPLET
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