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.

COPYRIGHT © 1996.2010 Cuthbert Nyack.