Fourier Synthesis
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 sawtoothed wave is
The approximation improves as more oscillations are added.
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A sample session would be as follows:
•
To produce a sawtoothed wave, in the white box to the right of the word "Sin:" enter a formula
such as
1/x
or
(1^(x1))/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.
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 Fall '08
 MichaelFrumin
 Fourier Series, Tom Huber

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