Fourier Series Applet of 4 Segment Function.

Cuthbert Nyack

The diagram opposite shows a periodic function constructed from 4 straight line segments. With this simple shape, spectra of several functions can be studied eg. square, triangular, ramp etc by varying a to h. Spectra of odd and even functions and their combinations can also be investigated.

In the applet below the 8 scrollbars can be used to change the parameters a to h to produce different functions. Each parameter can be varied from -1 to +1.
Fn sets the function of the applet.
Fn = 0 shows the function reconstructed from its spectrum.
Fn = 1 to 6 show special cases of Fn = 0.
Fn = 7 shows the function represented as a sum of its even and odd parts.
Fn = 8 to 11 show special cases of Fn = 7.
Fn = 12 shows the function represented as a sum of its continuous and discontinuous parts.
Fn = 13 to 17 show special cases of Fn = 12.
Fn = 18 shows the function represented as a sum of its half wave symmetric and nonsymmetric parts.
Fn = 19 to 22 show special cases of Fn = 18.

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