Fourier Series, Even and odd Functions
Cuthbert Nyack
In this page, the decomposition of the Fourier series
into even and odd parts is studied.
Any Function can be represented by a sum of
even and odd parts
.
The even part can be represented by the Fourier Series
and the odd part can be represented by the Fourier Series.
A simple example is shown below.
Other examples can be seen by changing the parameters in the
applet below. The pulse is in red, its even part in cyan
and its odd part in pink. The oscillations on the even and odd
parts are artefacts of the way they are calculated.
Fn = 2 to 12 show special cases of Fn = 1.
Fn = 13 shows half wave symmetry. Fn = 14 to 17 show special cases
of Fn = 13.
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COPYRIGHT © 1996.2010 Cuthbert Nyack.